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On validity of the asymptotic expansion approach in contingent claim analysis. (English) Zbl 1091.91037

Summary: Kunitomo and Takahashi have proposed a new methodology, called small disturbance asymptotics, for the valuation problem of financial contingent claims when the underlying asset prices follow a general class of continuous Itô processes. It can be applicable to a wide range of valuation problems, including complicated contingent claims associated with the Black–Scholes model and the term structure model of interest rates in the Heath-Jarrow-Morton framework. Our approach can be rigorously justified by an infinite-dimensional analysis called the Watanabe-Yoshida theory on the Malliavin calculus recently developed in stochastic analysis.

MSC:

91B28 Finance etc. (MSC2000)
60H07 Stochastic calculus of variations and the Malliavin calculus
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References:

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