Computation in an Asymptotic Expansion Method

Computation in an Asymptotic Expansion Method

An asymptotic expansion scheme in finance initiated by Kunitomo and Takahashi [15] and Yoshida[68] is a widely applicable methodology for analytic approximation of the expectation of a certain functional of diffusion processes. [46], [47] and [53] provide explicit formulas of conditional expectations necessary for the asymptotic expansion up to the third order. In general, the crucial step in p...

The Asymptotic Expansion Method via Symbolic Computation

The origin of symbolic manipulation derives from the sheer magnitude of the work involved in the building of perturbation theories, which made inevitable that scientific community became interested in the possibility of constructing those theories with the help of computers. Perturbation theories for differential equations containing a small parameter are quite old. The small perturbation theor...

Option Pricing in HJM Model using an Asymptotic Expansion Method

* This is the English version of the paper titled "Option Pricing in HJM Model using an Asymptotic Expansion Method" published in December 2004. This paper represents the personal views of the authors and is NOT the official view of the Financial Services Agency or the Financial Research and Training Center. † In preparing this paper, valuable advice was provided by Mr. Yoshihiko Uchida (Instit...

Matched asymptotic expansion method for an homogenized interface model

An asymptotic expansion inspired by Ramanujan yRichard

Corollary 2, Entry 9, Chapter 4 of Ramanujan's rst notebook claims that 1 X k=1 (?1) k?1 nk x k k! n ln x + as x ! 1. This is known to be correct for the case n = 1, but incorrect for n 3. We show that the result is correct for n = 2. We also consider the order of the error term, and discuss a diierent, correct generalisation of the case n = 1.