Higher-order error estimates of the discrete-time Clark--Ocone formula

Tsubasa Nishimura; Kenji Yasutomi; Tomooki Yuasa

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arXiv · 2101.07087

Higher-order error estimates of the discrete-time Clark--Ocone formula

Tsubasa Nishimura·Kenji Yasutomi·Tomooki Yuasa

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Abstract

In this article, we investigate the convergence rate of the discrete-time Clark--Ocone formula provided by Akahori--Amaba--Okuma [1]. In that paper, they mainly focus on the $L_{2}$-convergence rate of the first-order error estimate related to the tracking error of the delta hedge in mathematical finance. Here, as two extensions, we estimate "the higher order error" for Wiener functionals with an integrability index $2$ and "an arbitrary differentiability index."

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Tsubasa Nishimura, Kenji Yasutomi, Tomooki Yuasa. 2021-01-18. Higher-order error estimates of the discrete-time Clark--Ocone formula. https://arxiv.org/abs/2101.07087

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