An Asymptotic Expansion Scheme for the Optimal Investment Problems

Akihiko Takahashi and Nakahiro Yoshida
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Akihiko Takahashi: Faculty of Economics and Graduate School of Mathematical Sciences, University of Tokyo
Nakahiro Yoshida: Graduate School of Mathematical Sciences, University of Tokyo

No CIRJE-F-248, CIRJE F-Series from CIRJE, Faculty of Economics, University of Tokyo

Abstract: 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, 1995, 1998, 2001), Yoshida (1992), Takahashi (1995, 1999),Takahashi and Yoshida (2001). In particular, we will explicitly derive a formula of the optimal portfolio associated with maximizing utility from terminal wealth in a nancial market with Markovian coe cients,and give a numerical example for a power utility function.

Pages: 35 pages
Date: 2003-11
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