We shall propose a new computational scheme with the asymptotic method to achieve variance reduction of Monte Carlo simulation for numerical analysis especially in finance. We not only provide general scheme of our method,@but also show its effectiveness through numerical examples such as...

We shall propose a new computational scheme for the evaluation of the optimal portfolio for investment.Our method is based on an extension of the asymptotic expansion approach which has been recently developed for pricing problems of the contingent claims' analysis by Kunitomo-Takahashi (1992,...

We shall propose a new computational scheme with the asymptotic method to achieve variance reduction of Monte Carlo simulation for numerical analysis especially in finance. We not only provide general scheme of our method, but also show its effectiveness through numerical examples such as...

All the financial practitioners are working in incomplete markets full of unhedgeable risk-factors. Making the situation worse, they are only equipped with the imperfect information on the relevant processes. In addition to the market risk, fund and insurance managers have to be prepared for...

In the paper, we propose a new calculation scheme for American options in the framework of a forward backward stochastic di erential equation (FBSDE). The well-known decomposition of an American option price with that of a European option of the same maturity and the remaining early exercise...

This paper presents a new asymptotic expansion method for pricing continuously monitoring barrier options. In particular, we develops a semi-group expansion scheme for the Cauchy-Dirichlet problem in the second-order parabolic partial differential equations (PDEs) arising in barrier option...

In the paper, we propose a new calculation scheme for American options in the framework of a forward backward stochastic differential equation (FBSDE). The wellknown decomposition of an American option price with that of a European option of the same maturity and the remaining early exercise...

This paper studies impacts of imperfect collateralization on derivatives values. Firstly, we present a general framework for the analysis in a multi-dimensional diffusion setting, and then calclate pre-default values of forwards and options for the numerical experiments. In particular, we...