Thetransitiontonet-zeroemissionsinEuropeisdeterminedbyapatchworkofcountry-levelandEUwide policy, creating coordination challenges in an interconnected system. We use an optimisation model to mapoutnear-optimal energy system designs for 2050, focussing on the planning flexibility of individual regions while maintaining overall system robustness against different weather years, cost assumptions, and land use limitations. Our results reveal extensive flexibility at a regional level, where only few technologies (solar around the Adriatic and wind on the British Isles and in Germany) cannot be substituted. National policymakers can influence renewable energy export and hydrogen strategies significantly, provided they coordinate this with the remaining European system. However, stronger commitment to solar in Southern Europe and Germany unlocks more design options for Europe overall. These results on regional trade-offs facilitate more meaningful policy discussions which are crucial in the transition to a sustainable energy system.
Vorobeva, Ekaterina; Eggen, Mari Dahl, Midtfjord, Alise Danielle, Benth, Fred Espen, Hupe, Patrick, Brissaud, Quentin, Orsolini, Yvan Joseph Georges Emile G. & Näsholm, Sven Peter (2024)
Estimating stratospheric polar vortex strength using ambient ocean-generated infrasound and stochastics-based machine learning
There are sparse opportunities for direct measurement of upper stratospheric winds, yet improving their representation in subseasonal-to-seasonal prediction models can have significant benefits. There is solid evidence from previous research that global atmospheric infrasound waves are sensitive to stratospheric dynamics. However, there is a lack of results providing a direct mapping between infrasound recordings and polar-cap upper stratospheric winds. The global International Monitoring System (IMS), which monitors compliance with the Comprehensive Nuclear-Test-Ban Treaty, includes ground-based stations that can be used to characterize the infrasound soundscape continuously. In this study, multi-station IMS infrasound data were utilized along with a machine-learning supported stochastic model, Delay-SDE-net, to demonstrate how a near-real-time estimate of the polar-cap averaged zonal wind at 1-hPa pressure level can be found from infrasound data. The infrasound was filtered to a temporal low-frequency regime dominated by microbaroms, which are ambient-noise infrasonic waves continuously radiated into the atmosphere from nonlinear interaction between counter-propagating ocean surface waves. Delay-SDE-net was trained on 5 years (2014–2018) of infrasound data from three stations and the ERA5 reanalysis 1-hPa polar-cap averaged zonal wind. Using infrasound in 2019–2020 for validation, we demonstrate a prediction of the polar-cap averaged zonal wind, with an error standard deviation of around 12 m·s compared with ERA5. These findings highlight the potential of using infrasound data for near-real-time measurements of upper stratospheric dynamics. A long-term goal is to improve high-top atmospheric model accuracy, which can have significant implications for weather and climate prediction.
In this article, we investigate the mismatch of renewable electricity production to demand and how flexibility options enabling spatial and temporal smoothing can reduce risks of variability. As a case study we pick a simplified (partial) 2-region representation of the Norwegian electricity system and focus on wind power. We represent regional electricity production and demand through two stochastic processes: the wind capacity factors are modelled as a two-dimensional Ornstein–Uhlenbeck process and electricity demand consists of realistic base load and temperature-induced load coming from a deseasonalised autoregressive process. We validate these processes, that we have trained on historical data, through Monte Carlo simulations allowing us to generate many statistically representative weather years. For the investigated realisations (weather years) we study deviations of production from demand under different wind capacities, and introduce different scenarios where flexibility options like storage and transmission are available. Our analysis shows that simulated loss values are reduced significantly by cooperation between regions and either mode of flexibility. Combining storage and transmission leads to even more synergies and helps to stabilise production levels and thus reduces likelihoods of inadequacy of renewable power systems.
Benth, Fred Espen; Schroers, Dennis & Veraart, Almut E.D. (2024)
A feasible central limit theorem for realised covariation of SPDEs in the context of functional data
We suggest a new methodology for designing robust energy systems. For this, we investigate so-called near-optimal solutions to energy system optimisation models; solutions whose objective values deviate only marginally from the optimum. Using a refined method for obtaining explicit geometric descriptions of these near-optimal feasible spaces, we find designs that are as robust as possible to perturbations. This contributes to the ongoing debate on how to define and work with robustness in energy systems modelling.
We apply our methods in an investigation using multiple decades of weather data. For the first time, we run a capacity expansion model of the European power system (one node per country) with a three-hourly temporal resolution and 41 years of weather data. While an optimisation with 41 weather years is at the limits of computational feasibility, we use the near-optimal feasible spaces of single years to gain an understanding of the design space over the full time period. Specifically, we intersect all near-optimal feasible spaces for the individual years in order to get designs that are likely to be feasible over the entire time period. We find significant potential for investment flexibility, and verify the feasibility of these designs by simulating the resulting dispatch problem with four decades of weather data. They are characterised by a shift towards more onshore wind and solar power, while emitting more than 50% less CO2 than a cost-optimal solution over that period.
Our work builds on recent developments in the field, including techniques such as Modelling to Generate Alternatives (MGA) and Modelling All Alternatives (MAA), and provides new insights into the geometry of near-optimal feasible spaces and the importance of multi-decade weather variability for energy systems design. We also provide an effective way of working with a multi-decade time frame in a highly parallelised manner. Our implementation is open-sourced, adaptable and is based on PyPSA-Eur.
Benth, Fred Espen & Krühner, Paul (2023)
Stochastic Models for Prices Dynamics in Energy and Commodity Markets An Infinite-Dimensional Perspective
Benth, Fred Espen & Lempa, Jukka (2023)
Hedging temperature risk with CDD and HDD temperature futures
The purpose of this paper is to present and discuss pedagogical frameworks and approaches to developing, delivering, and evaluating a new interdisciplinary course within the domain of energy informatics at both Master’s and PhD levels. This study is needed because many papers on sustainable energy engineering education concentrate on course content but provide very little information on the pedagogical methods employed to deliver that content. The proposed new course is called “smart energy and power systems modelling” and is aimed at discussing how mathematical optimization, in the context of computer science, can contribute to more effectively managing smart energy and power systems. Different pedagogical frameworks are discussed and adapted for the specific domain of energy informatics. An ASSURE model coupled with Bloom’s taxonomy is presented for the design of the course and identification of learning objectives; self-regulated learning strategies are discussed to enhance the learning process; a novel model called GPD (Gaussian Progression of Difficulty) for lecture planning was proposed; a teaching-research nexus is discussed for the course planning and enhancement. Adopting qualitative analyses and an inductive approach, this paper offers a thorough reflection on the strengths and weaknesses of the new course, together with improvement possibilities based on fieldwork and direct experience with the students and colleagues. Opportunities and challenges of interdisciplinary teaching are presented in light of real-world experience, with a particular focus on the interaction between mathematics and computer science to study the specific application of energy and power systems.
Schrader, Simon Elias & Benth, Fred Espen (2022)
A stochastic study of carbon emission reduction from electrification and interconnecting cable utilization. The Norway and Germany case
We provide a detailed analysis of the Gelfand integral on Fréchet spaces, showing among other things a Vitali theorem, dominated convergence and a Fubini result. Furthermore, the Gelfand integral commutes with linear operators. The Skorohod integral is conveniently expressed in terms of a Gelfand integral on Hida distribution space, which forms our prime motivation and example. We extend several results of Skorohod integrals to a general class of pathwise Gelfand integrals. For example, we provide generalizations of the Hida–Malliavin derivative and extend the integration-by-parts formula in Malliavin Calculus. A Fubini-result is also shown, based on the commutative property of Gelfand integrals with linear operators. Finally, our studies give the motivation for two existing definitions of stochastic Volterra integration in Hida space.
Benth, Fred Espen; Nunno, Giulia Di & Schroers, Dennis (2022)
A topological proof of Sklar's theorem in arbitrary dimensions
We propose a neural network architecture in infinite dimensional spaces for which we can show the universal approximation property. Indeed, we derive approximation results for continuous functions from a Fréchet space X into a Banach space Y. The approximation results are generalising the well known universal approximation theorem for continuous functions from Rn to R, where approximation is done with (multilayer) neural networks Cybenko (1989) Math. Cont. Signals Syst. 2, 303–314 and Hornik et al. (1989) Neural Netw., 2, 359–366 and Funahashi (1989) Neural Netw., 2, 183–192 and Leshno (1993) Neural Netw., 6, 861–867. Our infinite dimensional networks are constructed using activation functions being nonlinear operators and affine transforms. Several examples are given of such activation functions. We show furthermore that our neural networks on infinite dimensional spaces can be projected down to finite dimensional subspaces with any desirable accuracy, thus obtaining approximating networks that are easy to implement and allow for fast computation and fitting. The resulting neural network architecture is therefore applicable for prediction tasks based on functional data.
Benth, Fred Espen; Schroers, Dennis & Veraart, Almut E. D. (2022)
A weak law of large numbers for realised covariation in a Hilbert space setting
In this paper, we propose a new multivariate model for the dynamics of regional ocean freight rates. We show that a cointegrated system of regional spot freight rates can be decomposed into a common non-stationary market factor and stationary regional deviations. The resulting integrated CAR process is new to the literature. By interpreting the common market factor as the global arithmetic average of the regional rates, both the market factor and the regional deviations are observable which simplifies the calibration of the model. Moreover, forward contracts on the market factor can be traded in the Forward Freight Agreement (FFA) market. We calibrate the model to historical spot rate processes and illustrate the term structures of volatility and correlation between the regional prices and the market factor. Our model is an important contribution towards improved modelling and hedging of regional price risk when derivative market liquidity is concentrated in a single global benchmark.
Benth, Fred Espen & Suss, Andre (2018)
Continuous-Time Autoregressive Moving-Average Processes in Hilbert Space
Stochastic models for forward electricity prices are of great relevance nowadays, given the major structural changes in the market due to the increase of renewable energy in the production mix. In this study, we derive a spatio-temporal dynamical model based on the Heath-Jarrow-Morton (HJM) approach under the Musiela parametrization, which ensures an arbitrage-free model for electricity forward prices. The model is fitted to a unique data set of historical price forward curves. As a particular feature of the model, we disentangle the temporal from spatial (maturity) effects on the dynamics of forward prices, and shed light on the statistical properties of risk premia, of the noise volatility term structure and of the spatio-temporal noise correlation structures. We find that the short-term risk premia oscillates around zero, but becomes negative in the long run. We identify the Samuelson effect in the volatility term structure and volatility bumps, explained by market fundamentals. Furthermore we find evidence for coloured noise and correlated residuals, which we model by a Hilbert space-valued normal inverse Gaussian Lévy process with a suitable covariance functional.
(Best Energy Paper Award, ECOMFIN 2016, Paris)
Benth, Fred Espen; Eriksson, Marcus Karl Viren & Westgaard, Sjur (2017)
Stochastic Volatility Modeling of Emission Allowances Futures Prices in the European Union Emission Trading System Market
We conduct an empirical investigation of the logreturns of the futures prices of the European Union Emission Trading System emission certificates traded in the Nord Pool market between 2005 and 2013. We observe heaviness, skewness, and high kurtosis of these logreturns. We thus propose modeling the futures logprices using the Barndorff-Nielsen and Shephard (BNS) or the Heston stochastic volatility models.We carry out an empirical comparison between the performances of these models and investigate their stationary autocorrelation structure. In particular, as a consequence of allowing for skewness in the Heston model, we find analytical expressions for the autocorrelation function of the logreturns and their squares. Our analysis indicates the presence of short-range dependence in the observed futures logprice returns. We conclude that the BNS model better describes the empirical features of the observed futures prices than the Heston model. Our findings have relevance for the real option modeling of fossil-fueled power plants when considering emission costs.
Pircalabu, Anca & Benth, Fred Espen (2017)
A regime-switching copula approach to modeling day-ahead prices in coupled electricity markets
We propose and investigate a valuation model for the income of selling tradeable
green certificates (TGCs) in the Swedish–Norwegian market, formulated as a singular
stochastic control problem. Our model takes into account the production rate
of renewable energy from a “typical” plant, the price of TGCs and the cumulative
amount of certificates sold.We assume that the production rate has a dynamics given
by an exponential Ornstein–Uhlenbeck process, and the logarithmic TGC price has a
dynamics given by a Lévy process. For this class of dynamics, we find optimal decision
rules for the state variables and a closed-form solution to the control problem.
A case study of ICAP prices and wind production data from Denmark backs up our
model choice and shows the relevance of this pricing approach.
Benth, Fred Espen & Ibrahim, Noor Adilah (2017)
Stochastic modeling of photovoltaic power generation and electricity prices
We develop a general approach to portfolio optimization in futures markets. Following the Heath–Jarrow–Morton (HJM) approach, we model the entire futures price curve at once as a solution of a stochastic partial differential equation. We also develop a general formalism to handle portfolios of futures contracts. In the portfolio optimization problem, the agent invests in futures contracts and a risk-free asset, and her objective is to maximize the utility from final wealth. In order to capture self-consistent futures price dynamics, we study a class of futures price curve models which admit a finite-dimensional realization. More precisely, we establish conditions under which the futures price dynamics can be realized in finite dimensions. Using the finite-dimensional realization, we derive a finite-dimensional form of the portfolio optimization problem and study its solution. We also give an economic interpretation of the coordinate process driving the finite-dimensional realization.
Benth, Fred Espen; Kluppelberg, Claudia, Muller, Gernot & Vos, Linda (2014)
Futures pricing in electricity markets based on stable CARMA spot models
In this paper, we present a multi-factor continuous-time autoregressive moving-average (CARMA) model for the short and forward interest rates. This model is able to present an adequate statistical description of the short and forward rate dynamics. We show that this is a tractable term structure model and provides closed-form solutions to bond prices, yields, bond option prices, and the term structure of forward rate volatility. We demonstrate the capabilities of our model by calibrating it to a panel of spot rates and the empirical volatility of forward rates simultaneously, making the model consistent with both the spot rate dynamics and forward rate volatility structure.
Sørensen, Torquil Macdonald & Benth, Fred Espen (2013)
Levy process simulation by stochastic step functions
Ambit processes are general stochastic processes based on stochastic integrals with respect to Lévy bases. Due to their flexible structure, they have great potential for providing realistic models for various applications such as in turbulence and finance. This papers studies the connection between ambit processes and solutions to stochastic partial differential equations. We investigate this relationship from two angles: from the Walsh theory of martingale measures and from the viewpoint of the Lévy noise analysis.
Benth, Fred Espen & Henriksen, Pål Nicolai (2011)
Pricing of Basket Options Using Univariate Normal Inverse Gaussian Approximations
We propose a continuous-time autoregressive model for the temperature dynamics with volatility
being the product of a seasonal function and a stochastic process. We use the Barndorff-Nielsen
and Shephard model for the stochastic volatility. The proposed temperature dynamics is flexible
enough to model temperature data accurately, and at the same time being analytically tractable.
Futures prices for commonly traded contracts at the Chicago Mercantile Exchange on indices like
cooling- and heating-degree days and cumulative average temperatures are computed, as well as
option prices on them.
We consider the non-Gaussian stochastic volatility model of Barndorff-Nielsen and Shephard for the exponential mean-reversion model of Schwartz proposed for commodity spot prices. We analyze the properties of the stochastic dynamics, and show in particular that the log-spot prices possess a stationary distribution defined as a normal variance-mixture model. Furthermore, the stochastic volatility model allows for explicit forward prices, which may produce a hump structure inherited from the mean-reversion of the stochastic volatility. Although the spot price dynamics has continuous paths, the forward prices will have a jump dynamics, where jumps occur according to changes in the volatility process. We compare with the popular Heston stochastic volatility dynamics, and show that the Barndorff-Nielsen and Shephard model provides a more flexible framework in describing commodity spot prices. An empirical example on UK spot data is included.
Benth, Fred Espen; Härdle, Wolfgang Karl & Cabrera, Brenda Lopez (2011)
Benth, Fred Espen; Frestad, Dennis & Koekebakker, Steen (2010)
Modeling Term Structure Dynamics in the Nordic Electricity Swap Market
31(2) , s. 53- 86.
We analyze the daily returns of Nordic electricity swaps and identify significant risk premia in the short end of the market. On average, long positions in this part of the swap market yield negative returns. The daily returns are distinctively non-normal in terms of tail-fatness, but we find little evidence of asymmetry. We investigate if the flexible four-parameter class of normal inverse Gaussian (NIG) distributions can capture the observed stylized facts and find that this class of distributions offers a remarkably improved fit relative to the normal distribution. We also compare the fit with that of the four-parameter class of stable distributions; the NIG law outperforms the stable law in the vast majority of cases. Thus, the NIG family of distributions, which allows for stochastic dynamics in terms of Levy processes that are suitable for pricing derivatives and Value-at-Risk measurements, is a serious candidate for modeling term structure dynamics in the Nordic electricity market.
Benth, Fred Espen; Nunno, Giulia Di & Khedher, Asma (2010)
Robustness of option prices and their deltas in markets modelled by jump-diffusions
(2)
Benth, Fred Espen; Koekebakker, Steen & Zakamouline, Valeri (2010)
A Continuous Time Model for Interest Rate with Autoregressive and Moving Average Components
Daily average wind speeds are dynamically modelled by a continuous-time autoregressive model with seasonal mean and volatility. Futures prices based on an index of aggregated wind speeds are derived, and it is shown that the Samuelson effect breaks down. The volatility of these futures will decrease when approaching maturity, an effect which is explained by the memory in higher-order autoregressive models. (C) 2008 Elsevier B.V. All rights reserved.
Benth, Fred Espen & Proske, Frank Norbert (2009)
Utility indifference pricing of interest rate guarantees
Stochastic modeling of financial electricity contracts
30(3) , s. 1116- 1157.
We discuss the modeling of electricity contracts traded in many deregulated power markets. These forward/futures type contracts deliver (either physically or financially) electricity over a specified time period, and is frequently referred to as swaps since they in effect represent an exchange of fixed for floating electricity price. We propose to use the Heath-Jarrow-Morton approach to model swap prices since the notion of a spot price is not easily defined in these markets. For general stochastic dynamical models, we connect the spot price, the instantaneous-delivery forward price and the swap price, and analyze two different ways to apply the Heath-Jarrow-Morton approach to swap pricing: Either one specifies a dynamics for the non-existing instantaneous-delivery forwards and derives the implied swap dynamics, or one models directly on the swaps. The former is shown to lead to quite complicated stochastic models for the swap price, even when the forward dynamics is simple. The latter has some theoretical problems due to a no-arbitrage condition that has to be satisfied for swaps with overlapping delivery periods. To overcome this problem, a practical modeling approach is analyzed. The market is supposed only to consist of non-overlapping swaps, and these are modelled directly. A thorough empirical study is performed using data collected from Nord Pool. Our investigations demonstrate that it is possible to state reasonable models for the swap price dynamics which is analytically tractable for risk management and option pricing purposes, however, this is an area of further research. (c) 2007 Elsevier B.V. All rights reserved.
Benth, Fred Espen; Cartea, Alvaro & Kiesel, Ruediger (2008)
Pricing forward contracts in power markets by the certainty equivalence principle: Explaining the sign of the market risk premium
Barth, Andrea; Benth, Fred Espen & Potthoff, Juergen (2008)
HEDGING OF SPATIAL TEMPERATURE RISK WITH MARKET-TRADED FUTURES
The main objective of this work is to construct optimal temperature futures
from available market-traded contracts to hedge spatial risk. Temperature dynamics are
modelled by a stochastic differential equation with spatial dependence. Optimal positions
in market-traded futures minimizing the variance are calculated. Examples with numerical
simulations based on a fast algorithm for the generation of random fields are presented.
Benth, Fred Espen; Benth, Jurate S & Koekebakker, Steen (2008)
Stochastic Modelling of Electricity and Related Markets
Benth, Fred Espen; Groth, Martin & Kufakunesu, Rodwell (2007)
Valuing Volatility and Variance Swaps for a Non-Gaussian Ornstein-Uhlenbeck Stochastic Volatility Model
The volatility of temperature and pricing of weather derivatives
7(5) , s. 553- 561.
We propose an Ornstein-Uhlenbeck process with seasonal volatility to model the time dynamics of daily average temperatures. The model is fitted to approximately 45 years of daily observations recorded in Stockholm, one of the European cities for which there is a trade in weather futures and options on the Chicago Mercantile Exchange. Explicit pricing dynamics for futures contracts written on the number of heating/cooling degree-days (so-called HDD/CDD futures) and the cumulative average daily temperature (so-called CAT futures) are calculated, along with a discussion on how to evaluate call and put options with these futures as underlying.
Benth, Fred Espen; Kallsen, Jan & Meyer-Brandis, Thilo (2007)
A Non-Gaussian Ornstein-Uhlenbeck process for electricity spot price modeling and derivatives pricing
Benth, Fred Espen; Groth, Martin & Kufakunesu, Rodwell (2007)
Valuing Volatility and Variance Swaps for a Non-Gaussian Ornstein-Uhlenbeck Stochastic Volatility Model
14(4) , s. 347- 363.
Benth, Fred Espen; Nunno, Giulia Di, Lindstrøm, Tom, Øksendal, Bernt & Zhang, Tusheng (2007)
Stochastic Analysis and Applications The Abel Symposium 2005 Proceedings of the Second Abel Symposium, Oslo, July 29 - August 4, 2005, held in honor of Kiyosi Itô
Benth, Fred Espen; Saltyte-Benth, Jurate & Koekebakker, Steen (2007)
Putting a price on temperature
34(4) , s. 746- 767.
Benth, Fred Espen; Ollmar, Fridthjof & Koekebakker, Steen (2007)
Extracting and applying smooth forward curves from average-based commodity contracts with seasonal variation
15(1) , s. 52- 66.
Benth, Fred Espen; Groth, Martin & Kettler, Paul Carlisle (2006)
A Quasi-Monte Carlo algorithm for the normal inverse Gaussian distribution and valuation of financial derivatives
9(6) , s. 843- 867.
Benth, Fred Espen & Saltyte-Benth, Jurate (2006)
Analytic approximation for the price dynamics of spark spread options
10(3)
Benth, Fred Espen & Saltyte-Benth, Jurate (2005)
Stochastic modelling of temperature variations with a view towards weather derivatives
12(1) , s. 53- 85.
Benth, Fred Espen & Karlsen, Kenneth Hvistendahl (2005)
A PDE representation of the density of the minimal entropy martingale measure in stochastic volatility markets
77(2) , s. 109- 137.
Benth, Fred Espen & Karlsen, Kenneth Hvistendahl (2005)
A note on Merton's portfolio selection problem for the Schwartz mean-reversion model
23
Benth, Fred Espen & Meyer-Brandis, Thilo (2005)
The density process of the minimal entropy martingale measure in a stochastic volatility model with jumps
In a market driven by a Lévy martingale, we consider a claim ;. We study the problem of minimal variance hedging and we give an explicit formula for the minimal variance portfolio in terms of Malliavin derivatives. We discuss two types of stochastic (Malliavin) derivatives for ;: one based on the chaos expansion in terms of iterated integrals with respect to the power jump processes and one based on the chaos expansion in terms of iterated integrals with respect to the Wiener process and the Poisson random measure components. We study the relation between these two expansions, the corresponding two derivatives, and the corresponding versions of the Clark-Haussmann-Ocone theorem.
Benth, Fred Espen; Ekeland, Lars, Hauge, Ragnar & Nielsen, Bjørn Fredrik (2003)
A note on arbitrage-free pricing of forward contracts in energy markets
Arbitrage theory is used to price forward (futures) contracts in energy markets, where the underlying assets are non‐tradeable. The method is based on the so‐called ‘fitting of the yield curve’ technique from interest rate theory. The spot price dynamics of Schwartz is generalized to multidimensional correlated stochastic processes with Wiener and Lévy noise. Findings are illustrated with examples from oil and electricity markets.
Benth, Fred E.; Karlsen, Kenneth Hvistendahl & Reikvam, Kristin (2003)
A semilinear Black and Scholes partial differential equation for valuing American options
7(3) , s. 277- 298.
Benth, Fred Espen & Theting, Thomas Gorm (2003)
Some regularity results for the stochastic pressure equation of Wick-type
20(6) , s. 1191- 1223.
Benth, Fred Espen; Karlsen, Kenneth Hvistendahl & Reikvam, Kristin (2003)
A semilinear Black & Scholes partial differential equation for valuing American options
7(3) , s. 277- 298.
Benth, Fred E.; Karlsen, Kenneth Hvistendahl & Reikvam, Kristin (2002)
Portfolio optimization in a Lévy market with intertemporal substitution and transaction costs
74, s. 517- 569.
Benth, Fred Espen & Ng, Siu-Ah (2002)
Donsker's delta function and the covariance between generalized functionals
66(2) , s. 1- 13.
Benth, Fred Espen; Karlsen, Kenneth Hvistendahl & Reikvam, Kristin (2002)
Portfolio optimization in a Levy market with intertemporal substitution and transaction costs
74(3-4) , s. 517- 569.
Benth, Fred E.; Karlsen, Kenneth Hvistendahl & Reikvam, Kristin (2001)
Optimal portfolio management rules in a non-Gaussian market with durability and intertemporal substitution
5(4) , s. 447- 467.
Benth, Fred E.; Karlsen, Kenneth Hvistendahl & Reikvam, Kristin (2001)
Optimal portfolio selection with consumption and nonlinear integro-differential equations with gradient constraint: A viscosity solution approach
5(3) , s. 275- 303.
Benth, Fred Espen; Karlsen, Kenneth Hvistendahl & Reikvam, Kristin (2001)
A note on portfolio management under non-Gaussian logreturns
4(5) , s. 711- 732.
Benth, Fred Espen (2001)
On weighted L2(Omega)-spaces, their duals and Ito integration
19(3) , s. 329- 341.
Benth, Fred E.; Karlsen, Kenneth Hvistendahl & Reikvam, Kristin (2001)
A note on portfolio management under non-Gaussian logreturns
The Metropolis Adjusted Langevin Algorithm (MALA) samples from complex multivariate densities π. The proposal density is based on a discretized version of a Langevin diffusion, and is well defined only for continuously differentiable densities π. We propose a modified MALA algorithm when this condition is not fulfilled or when π has very rapid variations. The algorithm is illustrated on the Strauss model, for which two different classes of smoothing are proposed. In these examples smoothing gives advantages in terms of reduced asymptotic variance.
Benth, Fred Espen & Gjessing, Håkon K (2000)
A nonlinear parabolic equation with noise. A reduction method
12(4) , s. 385- 401.
Benth, Fred Espen (1999)
The Gross derivative and generalized random variables
2(3) , s. 381- 396.
Abrahamsen, Petter & Benth, Fred Espen (1998)
Gaussian field with unknown trend conditioned on inequality data - Proceedings of the 4th annual conference of the International Association for Mathematical Geology
, s. 333- 338.
Benth, Fred Espen & Gjerde, Jon (1998)
A remark on the equivalence between Poisson and Gaussian stochastic partial differential equations
8, s. 179- 193.
Benth, Fred Espen; Deck, Thomas, Potthoff, Jurgen, Streit, Ludvig & Streit, Ludwig (1998)
Nonlinear evolution equations with gradient coupled noise
Explicit strong solutions of SPDEs with applications to non-linear filtering
51, s. 215- 242.
Benth, Fred Espen & Gjerde, Jon (1998)
Convergence rates for finite element approximations of stochastic partial differential equations
63, s. 313- 326.
Benth, Fred Espen; Deck, Thomas & Potthoff, Jurgen (1997)
A White Noise approach to a class of non-linear stochastic heat equations
146(2) , s. 382- 415.
Benth, Fred Espen (1997)
On the positivity of the stochastic heat equation
6, s. 127- 148.
Benth, Fred Espen & Potthoff, Jurgen (1996)
On the martingale property for generalized stochastic processes
58, s. 349- 367.
Benth, Fred Espen; Øksendal, Bernt, Ubøe, Jan & Zang, Tusheng (1996)
Wick products of complex valued random variables
Benth, Fred Espen (1996)
A generalized Feynman-Kac formula for the stochastic heat problem with anticipating initial conditions
Benth, Fred Espen (1994)
An explicit functional process solution to a stochastic partial differential equation with applications to nonlinear filtering
51, s. 195- 216.
Benth, Fred Espen (1994)
A Functional Process Solution to a Stochastic Partial Differential Equation with Applications to Nonlinear Filtering
1994(51)
Benth, Fred Espen & Timpel, Matthias (1994)
Topological aspects of the characterization of Hida distributions - A remark
51, s. 293- 299.
Benth, Fred Espen (1993)
Integrals in the Hida Distribution Space (S)*
8
Skogvoll, Vidar; Lindstrøm, Tom Louis, Benth, Fred Espen & Haraldsrud, Andreas (2024)
Real læring - Realistfabrikken: Hvordan lage matematiker
[Kronikk]
Benth, Fred Espen & Zeyringer, Marianne (2021)
Er de rekordhøye strømprisene verdt det?
[Kronikk]
Aarønæs, Lars; Benth, Fred Espen & Nunno, Giulia Di (2014)
Hvordan beregner vi framtida?
[Kronikk]
Benth, Fred Espen (2012)
Universities fear power of robot trading to lure maths talent
[Kronikk]
Benth, Fred Espen (2012)
Mindre risiko i strømmarkedet
[Kronikk]
Benth, Fred Espen (2012)
Matematikere foretrekkes til tunge IT oppgaver
[Kronikk]
Yngve, Vogt & Benth, Fred Espen (2009)
Shopper uvær
[Kronikk]
Benth, Fred Espen (2007)
Bankskandalen
[Kronikk]
Benth, Fred Espen (2004)
Kraftmarkedet: Opsjoner med spenning
[Kronikk]
Grochowicz, Aleksander; Greevenbroek, Koen van, Benth, Fred Espen & Zeyringer, Marianne (2023)
Intersecting Near-Optimal Spaces for Policy Information
[Conference Lecture]. Event
Eggen, Mari Dahl; Midtfjord, Alise Danielle, Vorobeva, Ekaterina, Benth, Fred Espen, Hupe, Patrick, Brissaud, Quentin, Orsolini, Yvan Joseph Georges Emile G., Pichon, Alexis Le, Listowski, Constantino & Näsholm, Sven Peter (2023)
Using a machine learning and stochastics-founded model to provide near real-time stratospheric polar vortex diagnostics based on high-latitude infrasound data
[Conference Lecture]. Event
Acoustic waves below the frequency limit of human hearing - infrasound - can travel for thousands of kilometres in the atmosphere. The global propagation signature of infrasound is highly sensitive to the wind structure of the stratosphere.
This work exploits processed continuous data from three high-latitude infrasound stations to characterize an aspect of the stratospheric polar vortex. Concretely, a mapping is developed which takes the infrasound data from these three stations as input and outputs an estimate of the polar cap zonal mean wind averaged over 60-90 degrees in latitude at the 1 hPa pressure level. This stratospheric diagnostic information is relevant to, for example, sudden stratospheric warming assessment and sub-seasonal prediction.
The considered acoustic data is within a low-frequency regime globally dominated by so-called microbarom infrasound, which is continuously radiated into the atmosphere due to nonlinear interaction between counter-propagating ocean surface waves.
We trained a stochastics-based machine learning model (delay-SDE-net) to map between a time series of five years (2014-2018) of processed infrasound data and the ERA5 (reanalysis-based) daily average polar cap wind at 1 hPa for the same period. The ERA5 data was hence treated as ground-truth. In the prediction, the delay-SDE-net utilizes time-lagged inputs and their dependencies, as well as the day of the year to account for seasonal differences. In the validation phase, the input was the 2019 and 2020 infrasound time series, and the model inference results in an estimate of the daily average polar cap wind time-series. This result was then compared to the ERA5 representation of the stratospheric diagnostic time-series for the same period.
The applied machine learning model is based on stochastics and allows for an interpretable approach to estimate the aleatoric and epistemic prediction uncertainties. It is found that the mapping, which is only informed of the trained model, the day of year, and the infrasound data from three stations, generates a 1 hPa polar cap average wind estimate with a prediction error standard deviation of around 10 m/s compared to ERA5.
Focus should be put on the winter months because this is when the coupling between the stratosphere and the troposphere can mostly influence the surface conditions and provide additional prediction skill, in particular during strong and weak stratospheric polar vortex regimes. The infrasound data is available in real-time, and we discuss how the developed approach can be extended to provide near real-time stratospheric polar vortex diagnostics.
Benth, Fred Espen (2022)
Pricing Options on Flow Forwards by Neural Networks in Hilbert Space
[Conference Lecture]. Event
Benth, Fred Espen (2022)
Pricing options on flow forwards by neural networks in Hilbert space
[Conference Lecture]. Event
Benth, Fred Espen (2022)
Modellering av risiko i energisystemer
[Conference Lecture]. Event
Zeyringer, Marianne; Benth, Fred Espen, Roithner, Maximilian, Grochowicz, Aleksander & Sirotko-Sibirskaya, Natalia (2022)
Climate-resilient net-zero energy system design
[Lecture]. Event
Benth, Fred Espen (2022)
Klima og vær - data og risiko
[Conference Lecture]. Event
Grochowicz, Aleksander; Greevenbroek, Koen van, Benth, Fred Espen & Zeyringer, Marianne (2022)
Intersecting near-optimal spaces for robust energy systems
[Conference Lecture]. Event
Benth, Fred Espen & Zeyringer, Marianne (2021)
Uncertain energy systems
[Conference Lecture]. Event
Benth, Fred Espen (2021)
Hedging volumetric risk in renewable energy markets
[Conference Lecture]. Event
Benth, Fred Espen (2021)
Pathwise Gaussian Volterra processes in Hilbert space
Infinite dimensional Heston model and sensitivity analysis
[Conference Lecture]. Event
Benth, Fred Espen & Zeyringer, Marianne (2021)
Uncertain Energy Systems
[Conference Lecture]. Event
Benth, Fred Espen (2021)
Pathwise Gaussian Volterra processes in Hilbert space
[Conference Lecture]. Event
Benth, Fred Espen (2019)
Stochastic volatility in energy markets
[Conference Lecture]. Event
Benth, Fred Espen (2019)
Stochastic volatility in energy and commodity markets
[Conference Lecture]. Event
Benth, Fred Espen (2019)
Stochastic volatility in commodity markets
[Conference Lecture]. Event
Benth, Fred Espen (2018)
Stochastic integration for BSS processes
[Conference Lecture]. Event
Benth, Fred Espen (2018)
Cointegration in continuous time
[Conference Lecture]. Event
Benth, Fred Espen (2018)
Ambit fields and stochastic integration
[Conference Lecture]. Event
Benth, Fred Espen (2018)
Polynomial processes in Banach space
[Conference Lecture]. Event
Benth, Fred Espen (2018)
Cointegration in continuous time in commodity markets
[Conference Lecture]. Event
Benth, Fred Espen (2018)
Stochastic volatility modeling in power markets
[Lecture]. Event
Benth, Fred Espen (2017)
Continuous-time cointegration for factor models
[Conference Lecture]. Event
Benth, Fred Espen (2017)
Stochastic volatility for the forward price dynamics
[Conference Lecture]. Event
Benth, Fred Espen (2017)
CARMA processes in Hilbert space
[Conference Lecture]. Event
Benth, Fred Espen (2017)
Modelling stochastic volatility in forward markets
[Conference Lecture]. Event
Benth, Fred Espen (2016)
Cointegration in continuous time -- commodity spot and forward markets
[Conference Lecture]. Event
Ådland, Roar Os; Koekebakker, Steen & Benth, Fred Espen (2016)
Multivariate modelling of regional ocean freight rates
[Conference Lecture]. Event
Benth, Fred Espen (2016)
Ornstein-Uhlenbeck processes in Hilbert space - analysis and application
[Conference Lecture]. Event
Benth, Fred Espen (2016)
Stochastic modelling of energy markets
[Conference Lecture]. Event
Benth, Fred Espen (2016)
Modelling in energy markets
[Conference Lecture]. Event
Benth, Fred Espen (2015)
Forsikrer seg mot fornybar risiko
[Professional Article].
Benth, Fred Espen (2015)
Pricing and modelling electricity derivatives - cointegration and risk premia
[Conference Lecture]. Event
Benth, Fred Espen (2015)
Stochastic volatility in energy forward price models
[Conference Lecture]. Event
Benth, Fred Espen (2015)
Kriging smooth futures curves
[Report Research].
Benth, Fred Espen (2015)
Modelling energy forward prices - representation of ambit fields
[Conference Lecture]. Event
Benth, Fred Espen (2015)
Representation of Ambit Fields
[Conference Lecture]. Event
Benth, Fred Espen (2015)
CMA: Erfaringer med forskning på tvers og på langs i en SFF
[Lecture]. Event
Benth, Fred Espen (2014)
Stochastic volatility in energy markets
[Lecture]. Event
Benth, Fred Espen (2014)
Modelling of stochastic volatility and correlation in energy markets
[Lecture]. Event
Benth, Fred Espen (2014)
Stochastic partial differential equations in weather markets
[Conference Lecture]. Event
Benth, Fred Espen (2014)
Modelling of the risk premium in energy markets
[Conference Lecture]. Event
Benth, Fred Espen (2013)
A note on co-integration in commodity markets
[Conference Lecture]. Event
Benth, Fred Espen (2013)
Pricing and hedging average-based options in energy markets
[Conference Lecture]. Event
Benth, Fred Espen (2013)
A general approach to pricing in energy and weather markets
[Conference Lecture]. Event
Benth, Fred Espen (2013)
Modelling energy forward markets
[Conference Lecture]. Event
Eyjolfsson, Heidar & Benth, Fred Espen (2013)
Simulation of volatility modulated Volterra processes using hyperbolic stochastic partial differential equations
[Report Research].
We propose a finite difference scheme to simulate solutions to a certain type of hyperbolic stochastic partial differential equation (SPDE). These solutions can in turn estimate so called volatility modulated Volterra (VMV) processes and Levy semistationary (LSS) processes, which is a class of processes that have been employed to model turbulence, tumor growth and electricity forward and spot prices. We will see that our finite difference scheme converges to the solution of the SPDE as we take finer and finer partitions for our finite difference scheme in both time and space. Finally we will consider some examples from the energy finance literature.
Eyjolfsson, Heidar; Benth, Fred Espen & Veraart, Almut E. D. (2013)
Approximating Levy Semistationary processes via Fourier methods in the context of power markets
[Report Research].
The present paper discusses Levy semistationary processes in the context of power markets. A Fourier simulation scheme for obtaining trajectories of these processes is discussed and its rate of convergence is analysed. Finally we put our simulation scheme to work for simulating the price of path dependent options.
Benth, Fred Espen (2013)
Risikostyring i energimarkedet
[Conference Lecture]. Event
Benth, Fred Espen (2013)
Modelling forward prices in energy markets
[Conference Lecture]. Event
Benth, Fred Espen (2013)
Stationarity and risk premium in power markets
[Conference Lecture]. Event
Benth, Fred Espen (2013)
Modelling and pricing in energy and weather markets
[Conference Lecture]. Event
Benth, Fred Espen (2013)
"Financial engineering": hvordan kontrollere risiko i dagens energimarkeder
[Lecture]. Event
Benth, Fred Espen (2013)
A note on co-integration in commodity markets
[Conference Lecture]. Event
Benth, Fred Espen (2013)
The stochastics of energy markets
[Conference Lecture]. Event
Benth, Fred Espen (2013)
Hint og tips for skriving av vitenskapelige artikler
Benth, Fred Espen; Nunno, Giulia Di & Khedher, Asma (2010)
A note on convergence of option prices and their Greeks for Lévy models
[Report Research].
Zakamouline, Valeri; Koekebakker, Steen & Benth, Fred Espen (2010)
A Continuous Time Model for Interest Rate with Autoregressive and Moving Average Components
[Conference Lecture]. Event
Benth, Fred Espen (2010)
Ambit fields and stochastic partial differential equations
[Conference Lecture]. Event
Benth, Fred Espen (2010)
Weather derivatives: modeling and pricing
[Conference Lecture]. Event
Benth, Fred Espen (2010)
Modeling energy markets by ambit processes
[Conference Lecture]. Event
Benth, Fred Espen (2010)
The information premium in electricity markets: theory and empirics
[Conference Lecture]. Event
Benth, Fred Espen (2010)
Electricity forward contracts
Benth, Fred Espen (red.). Electricity forward contracts
Benth, Fred Espen (2010)
Option pricing: general principles
Benth, Fred Espen (red.). Option pricing: general principles
Benth, Fred Espen (2010)
Energy Finance - seen from the east side of the t-bane
[Lecture]. Event
Benth, Fred Espen (2010)
Pricing energy forward contracts -- the risk premium
[Conference Lecture]. Event
Benth, Fred Espen (2010)
On Forward Price Modeling in Power Markets
[Professional Article]. , s. 93- 122.
Benth, Fred Espen (2009)
Spot price modelling in energy markets
[Conference Lecture]. Event
Benth, Fred Espen (2009)
The volatility of temperature, pricing of weather derivatives and hedging of spatial temperature risk
[Conference Lecture]. Event
Benth, Fred Espen (2009)
Pricing electricity forwards -- the risk premium
[Conference Lecture]. Event
Benth, Fred Espen (2009)
Pricing electricity forwards, explaining the risk premium
[Conference Lecture]. Event
Benth, Fred Espen (2009)
Stochastic volatility modelling in energy markets
[Conference Lecture]. Event
Benth, Fred Espen & Meyer-Brandis, Thilo (2008)
The information premium in electricity markets
[Report Research].
Benth, Fred Espen (2008)
Forward price modelling in electricity
[Conference Lecture]. Event
Benth, Fred Espen (2008)
Modelling the electricity market
[Conference Lecture]. Event
Benth, Fred Espen (2008)
Lectures on stochastic modelling of electricity markets
[Conference Lecture]. Event
Benth, Fred Espen (2008)
Pricing electricity futures
[Conference Lecture]. Event
Benth, Fred Espen; Nunno, Giulia Di & Khedher, Asma (2008)
Robustness of delta hedging to model risk
[Conference Lecture]. Event
Benth, Fred Espen (2008)
Seasonal volatility and temperature derivatives
[Conference Lecture]. Event
Benth, Fred Espen (2008)
Pricing electricity futures: various approaches
[Conference Lecture]. Event
Benth, Fred Espen (2008)
Finanskrise(r) og matematisk finans
[Lecture]. Event
Benth, Fred Espen (2008)
Approaches to forward pricing in electricity markets
[Conference Lecture]. Event
Benth, Fred Espen (2008)
Pricing of electricity futures - the risk premium -
[Conference Lecture]. Event
Benth, Fred Espen (2008)
Spatial risk and temperature derivatives
[Conference Lecture]. Event
Benth, Fred Espen (2008)
Energy markets and modelling of risk
[Lecture]. Event
Benth, Fred Espen (2007)
Temperature derivatives and spatial risk
[Conference Lecture]. Event
Benth, Fred Espen (2007)
Modelling of electricity markets
[Conference Lecture]. Event
Benth, Fred Espen (2007)
Spatial risk in markets for temperature
[Conference Lecture]. Event
Benth, Fred Espen (2007)
Applications of Monte Carlo methods in finance
[Conference Lecture]. Event
Benth, Fred Espen (2007)
Modelling the forward curve in the Nord Pool market
[Conference Lecture]. Event
Benth, Fred Espen (2007)
The risk premium and future information in electricity markets
[Conference Lecture]. Event
Benth, Fred Espen (2007)
Spot price modelling in the energy markets
[Conference Lecture]. Event
Benth, Fred Espen (2007)
Options and the stochastic volatility model of Barndorff-Nielsen and Shephard
[Conference Lecture]. Event
Benth, Fred Espen (2007)
Modelling and Pricing in Energy Markets
[Conference Lecture]. Event
Benth, Fred Espen (2007)
Options and the Barndorff-Nielsen and Shephard stochastic volatility model
[Conference Lecture]. Event
Benth, Fred Espen (2007)
"Gratis lunsj" og finans
[Lecture]. Event
Benth, Fred Espen (2006)
Modelling and pricing in electricity markets
[Conference Lecture]. Event
Benth, Fred Espen (2006)
Modelling the temperature and pricing weather derivatives
[Conference Lecture]. Event
Benth, Fred Espen (2006)
Realopsjoner, finansielle opsjoner og partielle differensiallikninger
[Lecture]. Event
Benth, Fred Espen (2006)
Modelling the temperature and pricing weather derivatives
[Conference Lecture]. Event
Benth, Fred Espen (2006)
Modelling electricity forward prices
[Conference Lecture]. Event
Benth, Fred Espen (2006)
Modelling energy prices with stochastic processes
[Conference Lecture]. Event
Benth, Fred Espen (2006)
Stochastic modelling of electricity markets
[Conference Lecture]. Event
Benth, Fred Espen (2006)
Mathematical finance for energy markets: stochastic models and pricing of derivatives
[Conference Lecture]. Event
Benth, Fred Espen (2006)
Mathematical finance for energy markets: stochastic models and pricing of derivatives
[Conference Lecture]. Event
Benth, Fred Espen (2006)
Prising og sikring av garantier - det teoretiske grunnlaget i et praktisk perspektiv
[Lecture]. Event
Benth, Fred Espen (2006)
The volatility of temperature and pricing of weather derivatives
[Conference Lecture]. Event
Benth, Fred Espen (2006)
Modelling electricity forward prices
[Conference Lecture]. Event
Benth, Fred Espen (2006)
Portfolio optimization for stochastic volatility models and utility indifference pricing
[Conference Lecture]. Event
Benth, Fred Espen (2005)
Pricing of spark spread options
[Conference Lecture]. Event
Benth, Fred Espen (2005)
Modelling energies using stochastic processes
[Conference Lecture]. Event
Benth, Fred Espen & Saltyte-Benth, Jurate (2005)
Analytical approximation for the price dynamics of spark spread options
[Report Research].
Benth, Fred Espen & Proske, Frank (2005)
Arbitrage-free pricing of interest-rate guarantees based on the utility indifference method
[Report Research].
Benth, Fred Espen (2005)
A non-Gaussian volatility model, the minimal entropy martingale measure and option pricing
[Conference Lecture]. Event
Benth, Fred Espen (2005)
Option pricing in the stochastic volatility model of Barndorff-Nielsen and Shephard
[Conference Lecture]. Event
Benth, Fred Espen (2005)
Stochastic modelling of electricity markets
[Conference Lecture]. Event
Benth, Fred Espen (2005)
Stochastic modeling of electricity markets
[Conference Lecture]. Event
Benth, Fred Espen; Saltyte-Benth, Jurate & Jalinskas, Paulus (2005)
A spatial-temporal for temperature with seasonal variance
[Report Research].
Benth, Fred Espen (2005)
Modelling electricity forward contracts
[Conference Lecture]. Event
Aas, Kjersti; Dimakos, Xeni Kristine & Benth, Fred Espen (2005)
Modell og simuleringsverktøy for porteføljer sammensatt av ulike typer aktivaklasser
[Report Research].
Benth, Fred Espen; Groth, Martin & Kettler, Paul Carlisle (2005)
A quasi-Monte Carlo algorithm for the normal inverse Gaussian distribution and valuation of financial derivatives
[Report Research].
Benth, Fred Espen; Kallsen, Jan & Meyer-Brandis, Thilo (2005)
A non-Gaussian Ornstein-Uhlenbeck process for electricity spot price modelling and derivatives pricing
[Report Research].
Benth, Fred Espen & Koekebakker, Steen (2005)
Stochastic modeling of financial electricity contracts
[Report Research].
Benth, Fred Espen & Groth, Martin (2005)
The minimal entropy martingale measure and numerical option pricing for the Barndorff-Nielsen -- Shephard stochastic volatility model
[Report Research].
Benth, Fred Espen (2004)
Prising i vær- og elektrisitetsmarkeder
[Conference Lecture]. Event
Benth, Fred Espen (2004)
Pricing in Electricity and Weather Markets
[Conference Lecture]. Event
Benth, Fred Espen (2004)
Det nordiske elektrisitetsmarkedet NordPool - Hedging og prising
[Lecture]. Event
Benth, Fred Espen & Galdal, Helge (2004)
Industridag med fokus på modellering av risiko i elektrisitetsmarkedet
[Popular Science Article]. (6) , s. 98- 99.
Benth, Fred Espen (2004)
Modelling of spot and forward contracts in weather and electricity markets
[Conference Lecture]. Event
Benth, Fred Espen (2004)
A stochastic temperature dynamics with applications to weather derivatives pricing
[Conference Lecture]. Event
Benth, Fred Espen & Meyer-Brandis, Thilo (2004)
Inidfference pricing and the minimal entropy martingale measure in a stochastic volatility model with jumps
[Report Research].
Benth, Fred Espen (2004)
Pricing in Electricity and Weather Markets
[Conference Lecture]. Event
Benth, Fred Espen & Karlsen, Kenneth Hvistendahl (2003)
A pde representation of the density of the minimal entropy martingale measure in stochastic volatility markets
[Report Research].
Benth, Fred Espen (2003)
Matematisk finans
[Lecture]. Event
Benth, Fred Espen (2003)
Why pde's in finance
[Lecture]. Event
Benth, Fred Espen (2003)
Bruk av matematikk i finansindustrien
[Lecture]. Event
Benth, Fred Espen (2003)
Options, portfolios and risk evaluation in energy markets
[Conference Lecture]. Event
Benth, Fred Espen (2003)
The minimal entropy martingale measure and a nonlinear pde
[Conference Lecture]. Event
Benth, Fred Espen (2003)
Choosing and evaluating stochastic processes for pricing in electricity markets
[Conference Lecture]. Event
Benth, Fred Espen (2002)
Renter
[Conference Lecture]. Event
Benth, Fred Espen (2002)
Merton's portfolio optimization problem and non-Gaussian stochastic volatility
[Conference Lecture]. Event
Benth, Fred Espen (2002)
Risikoevaluering og optimering av porteføljer
[Lecture]. Event
Benth, Fred Espen (2002)
End-user portfolios. Where is theory today?
[Conference Lecture]. Event
Benth, Fred Espen (2002)
Kan du blir rik på matematikk?
[Lecture]. Event
Benth, Fred Espen (2002)
Arbitrage-free pricing of forward contracts in energy markets. - Heavy tailed spot price models -
[Conference Lecture]. Event
Benth, Fred Espen (2002)
Er det lurt å investere i aksjer?
[Lecture]. Event
Benth, Fred Espen (2002)
Matematisk finans - Innføring i opsjonsteori med stokastisk analyse
[Textbook].
Bølviken, Erik & Benth, Fred Espen (2002)
Evaluation of risk in financial portfolios
[Report Research].
Benth, Fred Espen (2002)
Smakebiter fra finansmatematikken
[Lecture]. Event
Benth, Fred Espen (2001)
Ambit process in energy markets
[Conference Lecture]. Event
Benth, Fred E.; Karlsen, Kenneth Hvistendahl & Reikvam, Kristin (2001)
On the existence of optimal controls for a singular stochastic control problem in finance
[Conference Lecture]. Event
Benth, Fred Espen (2001)
Stokastiske modeller for verdipapirer og renteteori
[Conference Lecture]. Event
Dahl, Lars Oswald & Benth, Fred Espen (2001)
Valuation of asian basket options with quasi-monte carlo techniques and singular value decomposition
[Report Research].
Benth, Fred Espen (2001)
Optimal portfolios and Levy processes
[Conference Lecture]. Event
Benth, Fred Espen; Nunno, Giulia Di, Løkka, Arne, Øksendal, Bernt & Proske, Frank Norbert (2001)
Explicit Representation of the Minimal Variance Portfolio in Lévy Markets
[Report Research].
In a market driven by a Lévy martingale, we consider a claim x. We study the problem of minimal variance hedging and we give an explicit formula for the minimal variance portfolio in terms of Malliavin derivatives. We discuss two types of stochastic (Malliavin) derivatives for x: one based on the chaos expansion in terms of iterated integrals with respect to the power jump processes and one based on the chaos expansion in terms of iterated integrals with respect to the Wiener process and the Poisson random measure components. We study the relation between these two expansions, the corresponding two derivatives and the corresponding versions of the Clark-Haussmann-Ocone theorem.
Benth, Fred Espen (2001)
En innføring i stokastisk renteteori
[Conference Lecture]. Event
Benth, Fred Espen (2000)
Monte Carlo Methods in Mathematical Finance
[Conference Lecture]. Event
Benth, Fred Espen (2000)
Portfolio management in non-Gaussian markets
[Conference Lecture]. Event
Benth, Fred Espen (2000)
Numerisk beregning av opsjonspriser ved bruk av Monte Carlo simuleringsteknikker
[Conference Lecture]. Event
Benth, Fred Espen (2000)
Portfolio optimization in Levy markets
[Conference Lecture]. Event
Benth, Fred Espen (2000)
Optimering av aksjeporteføljer og stokastisk kontroll
[Conference Lecture]. Event
Benth, Fred Espen; Ekeland, Lars, Hauge, Ragnar, Holden, Lars, Nielsen, Bjørn Fredrik & Ekeland, Lars (2000)
Risk analysis of energy product portfolios
[Report Research].
Benth, Fred Espen (2000)
Matematisk finans
[Lecture]. Event
Benth, Fred Espen (2000)
Portfolio management in non-Gaussian markets
[Conference Lecture]. Event
Bølviken, Erik & Benth, Fred Espen (2000)
Quantification of risk in norwegian stocks via the normal inverse Gaussian distribution
[Conference Lecture]. Event
Benth, Fred Espen; Karlsen, Kenneth Hvistendahl & Reikvam, Kristin (2000)
On the existence of optimal controls for a singular stochastic control problem in finance
[Report Research].
Benth, Fred Espen (2000)
Optimal portfolio problems in Levy markets
[Conference Lecture]. Event
Benth, Fred Espen (2000)
Matematisk finans
[Lecture]. Event
Benth, Fred Espen (2000)
Portfolio management in non-Gaussian markets
[Conference Lecture]. Event
Abrahamsen, Petter & Benth, Fred Espen (2000)
Kriging with inequality constraints
[Report Research].
Benth, Fred Espen (2000)
Optimering av aksjeporteføljer og stokastisk kontroll
[Conference Lecture]. Event
Benth, Fred Espen (2000)
Investering under usikkerhet
[Conference Lecture]. Event
Benth, Fred Espen; Gjerde, Jon & Sannan, Sigurd (2000)
Portfolio Management and correlation
[Conference Lecture]. Event
Benth, Fred Espen (2000)
Optimal portfolios in Levy markets
[Conference Lecture]. Event
Benth, Fred Espen (2000)
Reservoir modelling and stochastic analysis
[Conference Lecture]. Event
Benth, Fred Espen (1999)
Optimal portfolio selection with consumption and nonlinear integro-differential equations with gradient constraints: a viscosity solution apporach
[Conference Lecture]. Event
Skare, Øivind; Benth, Fred Espen & Frigessi, Arnoldo (1999)
Smoothed Langevin proposals in Metropolis-Hastings algorithms
[Report Research].
Benth, Fred Espen (1999)
1: Portfolio optimization and consumption with intertemporal substitution 2: Merton's problem and the normal inverse Gaussian distribution - A case study -
[Conference Lecture]. Event
Benth, Fred Espen (1998)
Ikke lineær filterteori og hvit støy analyse
[Conference Lecture]. Event
Benth, Fred Espen & Mostad, Petter F. (1998)
Manual for BAYKRIG 3.0
[Report Research].
Sannan, Sigurd; Benth, Fred Espen & Gjerde, Jon (1998)
Prodsim 98 - Et verktøy for stokastisk modellering av produksjonsprofiler
[Report Research].
Benth, Fred Espen & Mostad, Petter F. (1997)
Spatial data transformation and categorical variables
[Report Research].
Benth, Fred Espen (1997)
ProdSim97 - Et verktøy for stokastisk simulering av produksjonsprofiler. Manual
[Report Research].
Benth, Fred Espen & Abrahamsen, Petter (1997)
Bayesian kriging of Gaussian fields constrained by inequality data
[Report Research].
Benth, Fred Espen (1997)
Generalized stochastic processes and stochastic partial differential equations
[Conference Lecture]. Event
Benth, Fred Espen (1997)
OBX-indeksen for 1995. Tilpasning med to ulike modeller og konsekvenser av dette
[Popular Science Article]. 7, s. 1- 7.
Benth, Fred Espen (1997)
Renteteori
[Report Research].
Benth, Fred Espen; Abrahamsen, Petter & Hauge, Ragnar (1997)
HCPV studium for PL199b
[Report Research].
Benth, Fred Espen (1997)
Utvidelse av Excel-pakken ProdSim og estimering av korrelasjon i Markov modell for prognosering
[Report Research].
Benth, Fred Espen & Gjerde, Jon (1997)
Manual for MrSim 97
[Report Research].
Benth, Fred Espen (1997)
Monte Carlo simulering av kontantstrømmen fra et oljefelt med usikker produksjonsrate
[Report Research].
Benth, Fred Espen (1997)
ProdSim97 - Et verktøy for stokastisk modellering av produksjonsprofiler. Modellbeskrivelse
[Report Research].
Mostad, Petter F. & Benth, Fred Espen (1997)
Manual for BAYKRIG 2.0
[Report Research].
Benth, Fred Espen (1996)
Simulering av produksjonsprofiler på norsk sokkel. Excel-pakken ProdSim
[Report Research].
Benth, Fred Espen & Holden, Lars (1996)
Some calculations of effective permeability
[Report Research].
Benth, Fred Espen (1996)
Some results from mathematical finance
[Report Research].
Benth, Fred Espen; Heggland, Knut & Holden, Lars (1996)
Estimering av usikkerheten i totalproduksjonen fra norsk sokkel
[Report Research].
Benth, Fred Espen (1995)
On the positivity of the stochastic heat equation
[Professional Article]. (21)
Aas, Kjersti; Abrahamsen, Petter & Benth, Fred Espen (1995)
HCPV evaluation of Troll Olje Gas Province
[Report Research].
Benth, Fred Espen & Streit, Ludwig (1995)
The Burgers Equation with a Non Gaussian Random Force
[Professional Article]. (17/95)
Benth, Fred Espen; Deck, Thomas, Potthoff, Jurgen & Streit, Ludwig (1995)
Nonlinear evolution equations with gradient coupled noise
[Professional Article]. (188)
Benth, Fred Espen (1995)
Stochastic partial differential equations and generalized stochastic processes
[Professional Article].
Benth, Fred Espen; Deck, Thomas & Potthoff, Jurgen (1995)
A white noise approach to a class of nonlinear stochastic heat equations
[Professional Article]. (194/95)
Benth, Fred Espen & Potthoff, Jurgen (1995)
On the martingale property for generalized stochastic processes
[Professional Article]. (195/95)
Benth, Fred Espen (1994)
A note on population growth in a crowded stochastic environment
[Professional Article]. (180/94)
Benth, Fred Espen & Gjessing, Hakon (1994)
A nonlinear parabolic equation with noise. A reduction method
[Professional Article]. (179)
Benth, Fred Espen (1993)
The Stochastic Cauchy Problem with Applications to Nonlinear Filtering
