New asymptotic expansion formula via Malliavin calculus and its application to rough differential equation driven by fractional Brownian motion (Forthcoming in Asymptotic Analysis)

Akihiko Takahashi and Toshihiro Yamada
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Akihiko Takahashi: The University of Tokyo, Japan
Toshihiro Yamada: Hitotsubashi University, Japan

No CARF-F-563, CARF F-Series from Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo

Abstract: This paper presents a novel generic asymptotic expansion formula of expectations of multidi-mensional Wiener functionals through a Malliavin calculus technique. The uniform estimate of the asymptotic expansion is shown under a weaker condition on the Malliavin covariance matrix of the target Wiener functional. In particular, the method provides a tractable expansion for the expectation of an irregular functional of the solution to a multidimensional rough differen-tial equation driven by fractional Brownian motion with Hurst index H

Pages: 20
Date: 2023-06, Revised 2024-11
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