Applications of the Asymptotic Expansion Approach based on Malliavin-Watanabe Calculus in Financial Problems

Naoto Kunitomo and Akihiko Takahashi
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Naoto Kunitomo: Graduate School of Economics, University of Tokyo, Japan
Akihiko Takahashi: Graduate School of Mathematical Sciences, University of Tokyo, Japan

Chapter 10 in Stochastic Processes and Applications to Mathematical Finance, 2004, pp 195-232 from World Scientific Publishing Co. Pte. Ltd.

Abstract: AbstractThis paper reviews the asymptotic expansion approach based on Malliavin-Watanabe Calculus in Mathematical Finance. We give the basic formulation of the asymptotic expansion approach and discuss its power and usefulness to solve important problems arisen in finance. As illustrations we use three major problems in finance and give some useful formulae and new results including numerical analyses.

Keywords: Stochastic Processes; Stochastic Differential Equations; Malliavin Calculus; Stochastic Control and Optimization; Functionals of Brownian Motions and Lévy Processes; Stochastic Models of Financial Market; Derivative Pricing; Hedging Problem (search for similar items in EconPapers)
Date: 2004
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