Chaotic Hedging with Iterated Integrals and Neural Networks

Code

• github.com/psc25/chaotichedging
  OfficialIn papernone★ 3

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 [1,), 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.

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