Simula@BI: Christa Cuchiero

Simula@BI invites Professor Christa Cuchiero, University of Vienna, to give a talk about Data Science/Machine learning.

Abstract

Signature methods represent a non-parametric way for extracting characteristic features from time series data which is essential in machine learning tasks. This explains why these techniques become more and more popular in econometrics, mathematical finance and dynamic modeling. We start by giving a brief introduction to signatures and then focus on their universal approximation property as linear regression basis of continuous path functionals. We then show their practical applicability for portfolio optimization in the spirit of stochastic portfolio theory. Indeed, we first introduce a novel class of portfolios which we call linear path-functional portfolios. These are portfolios which are determined by certain transformations of linear functions of a collections of feature maps that are non-anticipative path functionals of an underlying stochastic process. As main example for such feature maps we consider signature of the market weights. Relying on the universal approximation theorem we show that every continuous  (possibly path-dependent) portfolio function of the market weights can be uniformly approximated by signature portfolios. Besides these universality features, the main numerical advantage lies in the fact that several optimization tasks like maximizing expected logarithmic utility or mean-variance optimization within the class of linear path-functional portfolios reduces to a convex quadratic optimization problem, thus making it computationally highly tractable. We apply our method to real market data, indicating out-performance on the considered out-of-sample data even under transaction costs. The talk is based on joint work with Janka Möller.

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