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An Asymptotic Expansion Scheme for the Optimal Investment Problems

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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)

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.

Suggested Citation

  • Akihiko Takahashi & Nakahiro Yoshida, 2003. "An Asymptotic Expansion Scheme for the Optimal Investment Problems," CIRJE F-Series CIRJE-F-248, CIRJE, Faculty of Economics, University of Tokyo.
    • Handle: RePEc:tky:fseres:2003cf248
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    References listed on IDEAS

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    1. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    2. David Heath & Robert Jarrow & Andrew Morton, 2008. "Bond Pricing And The Term Structure Of Interest Rates: A New Methodology For Contingent Claims Valuation," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 13, pages 277-305, World Scientific Publishing Co. Pte. Ltd..
    3. Naoto Kunitomo & Akihiko Takahashi, 1998. "On Validity of the Asymptotic Expansion Approach in Contingent Claim Analysis," CIRJE F-Series 98-F-6, CIRJE, Faculty of Economics, University of Tokyo.
    4. Jérôme B. Detemple & Ren Garcia & Marcel Rindisbacher, 2003. "A Monte Carlo Method for Optimal Portfolios," Journal of Finance, American Finance Association, vol. 58(1), pages 401-446, February.
    5. Naoto Kunitomo & Akihiko Takahashi, 2001. "The Asymptotic Expansion Approach to the Valuation of Interest Rate Contingent Claims," Mathematical Finance, Wiley Blackwell, vol. 11(1), pages 117-151, January.
    6. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-257, August.
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