On validity of the asymptotic expansion approach in contingent claim analysis
On validity of the asymptotic expansion approach in contingent claim analysis
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DOI：
10.1214/aoap/1060202831
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发表时间：
2003-08
影响因子：
1.8
通讯作者：
N. Kunitomo;Akihiko Takahashi
中科院分区：
文献类型：
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作者：
N. Kunitomo;Akihiko Takahashi
Kunitomo和Takahashi(1995)和Takahashi(1997)提出了一种新的方法，称为小扰动渐近法，用于解决标的资产价格服从一般连续Ito过程的金融或有债权的估值问题。它可以适用于广泛的估值问题，包括与Black-Scholes模型和Heath-Jrow-Morton框架下的利率期限结构模型相关的复杂或有债权。我们的方法可以通过最近在随机分析中发展起来的Malliavin演算上的无限维分析(称为渡边-吉田理论)来严格证明。
Kunitomo and Takahashi (1995), and Takahashi (1997) 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 Ito 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.