Papers › Chaotic Hedging with Iterated Integrals and Neural Networks
Chaotic Hedging with Iterated Integrals and Neural Networks
Ariel Neufeld, Philipp Schmocker
In this paper, we derive an Lᵖ-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 Lᵖ-sense. Moreover, we can approximately solve the Lᵖ-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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