Mihriban Ceylan

Abstract

In recent years, signature-based methods have been very successfully applied in mathematical finance. At the very heart of these methods are universal approximation theorems, establishing that continuous functionals can be approximated arbitrarily well on compact sets by linear maps acting on signatures. However, in the context of mathematical finance, the restriction to compact sets causes a lack of theoretical justification for the use of signature based methods.

In this talk, we provide various global universal approximation theorems in the $L^p$-sense with respect to the Wiener measure. In particular, we demonstrate that functionals on rough path space can be approximated globally in the $L^p$-sense w.r.t. the Wiener measure. This allows, for instance, to approximate solutions to stochastic differential equations driven by Brownian motions by signature-based models, leading to a certain universality of signature-based models for financial markets.

Our speaker

Mihriban Ceylan is a Ph.D. student in Mathematics at the University of Mannheim, supervised by Prof. Dr. David Prömel. Her research focuses on rough path theory and signature-based methods, with an emphasis on universal approximation theorems for signatures - including global universality results and extensions to non-geometric rough path spaces.

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