Chaotic Hedging with Iterated Integrals and Neural Networks

Ariel Neufeld and Philipp Schmocker

Papers from arXiv.org

Abstract: In this paper, we derive an $L^p$-chaos expansion based on iterated Stratonovich integrals with respect to a given exponentially integrable continuous semimartingale. By omitting the orthogonality of the expansion, we show that every $p$-integrable functional, $p \in [1,\infty)$, can be approximated by a finite sum of iterated Stratonovich integrals. Using (possibly random) neural networks as integrands, we therefere obtain universal approximation results for $p$-integrable financial derivatives in the $L^p$-sense. Moreover, we can approximately solve the $L^p$-hedging problem (coinciding for $p = 2$ with the quadratic hedging problem), where the approximating hedging strategy can be computed in closed form within short runtime.

Date: 2022-09, Revised 2025-06
New Economics Papers: this item is included in nep-big, nep-cmp and nep-rmg
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