A Discrete-Time Clark–Ocone Formula and its Application to an Error Analysis

Jiro Akahori, Takafumi Amaba () and Kaori Okuma ()
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Takafumi Amaba: Ritsumeikan University
Kaori Okuma: Ritsumeikan University

Journal of Theoretical Probability, 2017, vol. 30, issue 3, 932-960

Abstract: Abstract In this paper, we will establish a discrete-time version of Clark(–Ocone–Haussmann) formula, which can be seen as an asymptotic expansion in a weak sense. The formula is applied to the estimation of the error caused by the martingale representation. Throughout, we use another distribution theory with respect to Gaussian rather than Lebesgue measure, which can be seen as a discrete Malliavin calculus.

Keywords: Discrete Clark–Ocone formula; Discrete Malliavin calculus; Sobolev differentiability-index is the rate of convergence; Primary 60H07; secondary 60F05; 60G42 (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s10959-016-0666-8

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