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

This 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 arised in nance. As illustrations we use three major problems in nance and give some useful formulae and new results including numerical analyses.

Dynamical Networks in Function Dynamics

As a first step toward realizing a dynamical system that evolves while spontaneously determining its own rule for time evolution, function dynamics (FD) is analyzed. FD consists of a functional equation with a self-referential term, given as a dynamical system of a 1-dimensional map. Through the time evolution of this system, a dynamical graph (a network) emerges. This graph has three interesting properties: i) vertices appear as stable elements, ii) the terminals of directed edges change in time, and iii) some vertices determine the dynamics of edges, and edges determine the stability of the vertices, complementarily. Two aspects of FD are studied, the generation of a graph (network) structure and the dynamics of this graph (network) in the system.Comment: 29 pages, 10 figure

"On Recent Developments in Mathematical Finance" (in Japanese)

We review some recent developments in mathematical finance and financial econometrics. In particular we discuss the asymptotic expansion approach recently proposed by Kunitomo and Takahashi (1995, 2001, 2002). Its mathematical validity is closely related to the Watanabe=Yoshida theory on Malliavin Calculus in Stochastic Analysis.

First record of the terrestrial amphipod, Talitroides alluaudi (Chevreux, 1896) (Crustacea, Amphipoda, Brevitalitridae), from Japan

We report Talitroides alluaudi (Chevreux, 1896) from Miyako Island, Ryukyu Islands, Japan. Although this terrestrial amphipod is distributed worldwide, including Indo-Pacific islands, Europe, and North and South America, the present specimens represent the first record of this species from Japanese islands. The cytochrome c oxidase subunit I (COI) sequence of a Miyako Island specimen was unique compared with the known COI sequences from Taiwanese and Bermudan populations

Cauer Ladder Network with Constant Basis Functions for Eddy Current Problems Involving Conductor Movement

This article proposes a Cauer ladder network with constant basis functions for eddy current problems involving translational movements. The analysis domain is decomposed into two domains: the stator part and the mover part. The Cauer ladder network method is applied to each domain to derive circuit parameters and corresponding basis functions to reconstruct the eddy current and compute the Lorentz force. Interactions between the two domains are modeled by current-controlled voltage sources connected to each stage of the Cauer ladder network. The gains of the current-controlled voltage sources are computed by numerical integration of the vector potential induced by the coil. An analysis of the TEAM Workshop Problem 28 was performed, and the results were validated by comparing them with those obtained by the commercially available software and showed a significant reduction in computational time