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Employee Profile

Fabian Andsem Harang

Professor - Department of Economics

Biography

I am working as a professor in mathematics at BI Norwegian Business School. I hold a Ph.D in Mathematics from the University of Oslo, where I specialized in stochastic analysis and financial mathematics.

My research is mostly focused around various topics in the field of stochastic analysis and rough path theory, and the application of these theories towards financial modelling and data science.

In the acameic year of 2023/2024 I am leading the Signatures for Images project at the Centre of Advanced Studies (CAS) together with Prof. Kurusch Ebrahimi-Fard (NTNU). See here for more information. I will therefore be located at The Norwegian Academy of Sciences and Letters during this year.

I am very interested in discussing applications of mathematical theory towards real cases arising in the financial industry, be it related to risk and portfolio management or trading. Please do not hestiate to get in touch if you are wondering about anything related to financial mathamtics or risk management.

See my personal homepage for more information fabianharang.xyz

Area of Expertise

Publications

Catellier, Rémi & Harang, Fabian Andsem (2023)

Pathwise regularization of the stochastic heat equation with multiplicative noise through irregular perturbation

Annales de l'I.H.P. Probabilites et statistiques, 59(3), s. 1572- 1609. Doi: 10.1214/22-AIHP1302

Existence and uniqueness of solutions to the stochastic heat equation with multiplicative spatial noise is studied. In the spirit of pathwise regularization by noise, we show that a perturbation by a sufficiently irregular continuous path establish wellposedness of such equations, even when the drift and diffusion coefficients are given as generalized functions or distributions. In addition we prove regularity of the averaged field associated to a Lévy fractional stable motion, and use this as an example of a perturbation regularizing the multiplicative stochastic heat equation.

Mork, Knut Anton; Harang, Fabian Andsem, Trønnes, Haakon Andreas & Bjerketvedt, Vegard Skonseng (2023)

Dynamic spending and portfolio decisions with a soft social norm

Journal of Economic Dynamics and Control, 151 Doi: 10.1016/j.jedc.2023.104667 - Full text in research archive

We explore the implications of a preference ordering for an investor-consumer with a strong preference for keeping consumption above an exogenous social norm, but who is willing to tolerate occasional dips below it. We do this by splicing two CRRA preference orderings, one with high curvature below the norm and the other with low curvature at or above it. We find this formulation appealing for many endowment funds and sovereign wealth funds, including the Norwegian Government Pension Fund Global, which inspired our research. We derive an analytical solution, which we use to describe key properties of the policy functions for consumption and portfolio allocation. We find that annual spending should not only be significantly lower than the expected financial return, but mostly also procyclical. In particular, financial losses should, as a rule, be followed by larger than proportional spending cuts, except when some smoothing is needed to keep spending from falling too far below the social norm. Yet, at very low wealth levels, spending should be kept particularly low in order to build sufficient wealth to raise consumption above the social norm. Financial risk taking should also be modest and procyclical, so that the investor sometimes may want to “buy at the top” and “sell at the bottom.” Many of these features are shared by habit-formation models and other models with some lower bound for consumption. However, our specification is more flexible and thus more easily adaptable to actual fund management. The nonlinearity of the policy functions may present challenges regarding delegation to professional managers. However, simpler rules of thumb with constant or slowly moving equity share and consumption-wealth ratio can reach almost the same expected discounted utility. Nevertheless, the constant levels will then look very different from the implications of expected CRRA utility or Epstein–Zin preferences in that consumption is much lower.

Harang, Fabian Andsem; Tindel, Samy & Wang, Xiaohua (2023)

Volterra Equations Driven by Rough Signals 3: Probabilistic Construction of the Volterra Rough Path for Fractional Brownian Motions

Journal of theoretical probability Doi: 10.1007/s10959-023-01251-y - Full text in research archive

Based on the recent development of the framework of Volterra rough paths (Harang and Tindel in Stoch Process Appl 142:34–78, 2021), we consider here the probabilistic construction of the Volterra rough path associated to the fractional Brownian motion with H > 1 2 and for the standard Brownian motion. The Volterra kernel k(t,s) is allowed to be singular, and behaving similar to |t − s| −γ for some γ ≥ 0. The construction is done in both the Stratonovich and Itô senses. It is based on a modified Garsia–Rodemich–Romsey lemma which is of interest in its own right, as well as tools from Malliavin calculus. A discussion of challenges and potential extensions is provided.

Bechtold, Florian; Harang, Fabian Andsem & Rana, Nimit (2023)

Non-linear Young equations in the plane and pathwise regularization by noise for the stochastic wave equation

Stochastics and Partial Differential Equations: Analysis and Computations Doi: 10.1007/s40072-023-00295-9 - Full text in research archive

We study pathwise regularization by noise for equations on the plane in the spirit of the framework outlined by Catellier and Gubinelli (Stoch Process Appl 126(8):2323–2366, 2016). To this end, we extend the notion of non-linear Young equations to a two dimensional domain and prove existence and uniqueness of such equations. This concept is then used in order to prove regularization by noise for stochastic equations on the plane. The statement of regularization by noise is formulated in terms of the regularity of the local time associated to the perturbing stochastic field. For this, we provide two quantified example: a fractional Brownian sheet and the sum of two one-parameter fractional Brownian motions. As a further illustration of our regularization results, we also prove well-posedness of a 1D non-linear wave equation with a noisy boundary given by fractional Brownian motions. A discussion of open problems and further investigations is provided.

Harang, Fabian Andsem & Mayorcas, Avi (2023)

Pathwise regularisation of singular interacting particle systems and their mean field limits

Stochastic Processes and their Applications, 159, s. 499- 540. Doi: 10.1016/j.spa.2023.02.005

Galeati, Lucio; Harang, Fabian Andsem & Mayorcas, Avi (2022)

Distribution dependent SDEs driven by additive fractional Brownian motion

Probability theory and related fields, s. 1- 59. Doi: 10.1007/s00440-022-01145-w - Full text in research archive

Harang, Fabian Andsem; Tindel, Samy & Wang, Xiaohua (2022)

Volterra equations driven by rough signals 2: higher order expansions

Stochastics and Dynamics Doi: 10.1142/S0219493723500028 - Full text in research archive

Galeati, Lucio; Harang, Fabian Andsem & Mayorcas, Avi (2022)

Distribution dependent SDEs driven by additive continuous noise

Electronic Journal of Probability (EJP), 27, s. 1- 38. Doi: 10.1214/22-EJP756 - Full text in research archive

Harang, Fabian Andsem; Nilssen, Torstein & Proske, Frank Norbert (2022)

GIRSANOV THEOREM FOR MULTIFRACTIONAL BROWNIAN PROCESSES

Stochastics: An International Journal of Probability and Stochastic Processes Doi: 10.1080/17442508.2022.2027948 - Full text in research archive

Galeati, Lucio & Harang, Fabian Andsem (2022)

Regularization of multiplicative SDEs through additive noise

The Annals of Applied Probability, 32(5), s. 3930- 3963. Doi: 10.1214/21-AAP1778 - Full text in research archive

Harang, Fabian Andsem & Perkowski, Nicolas (2021)

C ∞ - regularization of ODEs perturbed by noise

Stochastics and Dynamics, 21(8) Doi: 10.1142/S0219493721400104 - Full text in research archive

Harang, Fabian Andsem & Ling, Chengcheng (2021)

Regularity of Local Times Associated with Volterra–Lévy Processes and Path-Wise Regularization of Stochastic Differential Equations

Journal of theoretical probability Doi: 10.1007/s10959-021-01114-4 - Full text in research archive

Harang, Fabian Andsem & Catellier, Rémi (2021)

Pathwise regularization of the stochastic heat equation with multiplicative noise through irregular perturbation

arXiv.org

Harang, Fabian Andsem & Tindel, Samy (2021)

Volterra Equations Driven by Rough Signals

Stochastic Processes and their Applications, 142, s. 34- 78. Doi: 10.1016/j.spa.2021.08.001 - Full text in research archive

This article is devoted to the extension of the theory of rough paths in the context of Volterra equations with possibly singular kernels. We begin to describe a class of two parameter functions defined on the simplex called Volterra paths. These paths are used to construct a so-called Volterra-signature, analogously to the signature used in Lyon’s theory of rough paths. We provide a detailed algebraic and analytic description of this object. Interestingly, the Volterra signature does not have a multiplicative property similar to the classical signature, and we introduce an integral product behaving like a convolution extending the classical tensor product. We show that this convolution product is well defined for a large class of Volterra paths, and we provide an analogue of the extension theorem from the theory of rough paths (which guarantees in particular the existence of a Volterra signature). Moreover the concept of convolution product is essential in the construction of Volterra controlled paths, which is the natural class of processes to be integrated with respect to the driving noise in our situation. This leads to a rough integral given as a functional of the Volterra signature and the Volterra controlled paths, combined through the convolution product. The rough integral is then used in the construction of unique solutions to Volterra equations driven by Hölder noises with singular kernels. An example concerning Brownian noises and a singular kernel is treated.

Harang, Fabian Andsem & Benth, Fred Espen (2021)

Infinite Dimensional Pathwise Volterra Processes Driven by Gaussian Noise - Probabilistic Properties and Applications

Electronic Journal of Probability (EJP), 26 Doi: 10.1214/21-EJP683 - Full text in research archive

Bayer, Christian; Harang, Fabian Andsem & Pigato, Paolo (2021)

Log-modulated rough stochastic volatility models

SIAM Journal on Financial Mathematics, 12(3), s. 1257- 1284. Doi: 10.1137/20M135902X - Full text in research archive

Harang, Fabian Andsem; Lagunas, Marc & Ortiz-Latorre, Salvador (2021)

Self-Exciting Multifractional Processes

Journal of Applied Probability, 58(1), s. 22- 41. Doi: 10.1017/jpr.2020.88 - Full text in research archive

Amine, Oussama; Coffie, Emmanuel, Harang, Fabian Andsem & Proske, Frank Norbert (2020)

Bismut–Elworthy–Li formula, singular SDEs, fractional Brownian motion, Malliavin calculus, stochastic flows, stochastic volatility

Communications in Mathematical Sciences, 18(7), s. 1863- 1890. Doi: 10.4310/CMS.2020.v18.n7.a3

Harang, Fabian Andsem (2020)

An extension of the sewing lemma to hyper-cubes and hyperbolic equations driven by multi-parameter Young fields

Stochastics and Partial Differential Equations: Analysis and Computations Doi: 10.1007/s40072-020-00184-5

Harang, Fabian Andsem (2019)

Differential Equations Driven by Variable Order Hölder Noise, and the Regularizing Effect of Delay

Stochastics: An International Journal of Probability and Stochastic Processes Doi: 10.1080/17442508.2019.1602130

Amine, Oussama; Coffie, Emmanuel, Harang, Fabian Andsem & Proske, Frank Norbert (2018)

A Bismut-Elworthy-Li Formula for Singular SDE's Driven by a Fractional Brownian Motion and Applications to Rough Volatility Modeling

arXiv.org

Harang, Fabian Andsem (2024)

Signatures for Images

[Academic lecture]. Workshop on Stochastics, Memory and Roughness 2024.

Harang, Fabian Andsem (2022)

Pathwise regularization by noise for SDEs and SPDEs with multiplicative noise.

[Academic lecture]. XIV Brazilian Workshop on Mathematics.

Harang, Fabian Andsem (2021)

Pathwise regularization by noise for SDEs and SPDEs with multiplicative noise

[Academic lecture]. DNA Seminar.

Harang, Fabian Andsem (2021)

Log-modulated fractional Brownian motion and super rough volatility.

[Academic lecture]. 6th Berlin Workshop for Young Researchers on Mathematical Finance: 23-25.Aug.2021.

Harang, Fabian Andsem (2020)

Infinitely regularizing paths, and regularization by noise

[Academic lecture]. DNA seminar, Mathematics department, NTNU Trondheim.

Harang, Fabian Andsem (2020)

C^\infty regularization of ODEs perturbed by noise

[Academic lecture]. Young researchers between geometry and stochastic analysis.

Harang, Fabian Andsem (2020)

Volterra Equations driven by Rough Noise

[Academic lecture]. Seminar for Probability group at Université Nice-Sophia-Antipolis.

Harang, Fabian Andsem (2020)

Volterra Equations Driven by Rough Signals

[Academic lecture]. Seminar For Berlin Rough Paths Group.

Harang, Fabian Andsem (2020)

Infinitely regularising paths and regularisation by noise

[Academic lecture]. Oxford Stochastic Analysis and Mathematical Finance Seminar.

Harang, Fabian Andsem (2019)

Volterra equations driven by rough signals (2)

[Academic lecture]. CSA2019 - Conference in Stochastic Analysis - Risør.

Harang, Fabian Andsem (2019)

Volterra equations driven by rough signals

[Academic lecture]. Berlin -Oxford meeting, WIAS Berlin.

Harang, Fabian Andsem (2019)

A multi parameter sewing lemma, and applications

[Academic lecture]. Seminar at NTNU Trondhiem.

Harang, Fabian Andsem (2019)

A Multiparameter Sewing Lemma with applications

[Academic lecture]. Seminar at Purdue University, Indiana, USA.

Academic Degrees
Year Academic Department Degree
2018 University of Oslo, Department of mathematics Ph.D.
Work Experience
Year Employer Job Title
2023 - Present BI Norwegian Business School Professor of Mathematics
2021 - 2022 BI Norwegian Business School Associate Professor of Mathematics
2019 - 2021 University of Oslo Postdoctor