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Optimal Portfolios With Stochastic Short Rate: Pitfalls When The Short Rate Is Non-Gaussian Or The Market Price Of Risk Is Unbounded

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  • HOLGER KRAFT

    (Goethe-University, Department of Finance, Frankfurt am Main, Germany)

Abstract

The aim of this paper is to provide a survey of some of the problems occurring in portfolio problems with power utility, Non-Gaussian interest rates, and/or unbounded market price of risk. Using stochastic control theory, we solve several portfolio problems for different specifications of the short rate and the market price of risk. In particular, we consider a Gaussian model, the Cox-Ingersoll-Ross model, and squared Gaussian as well as lognormal specifications of the short rate. We find that even in a Gaussian framework the canonical candidate for the value function may not be finite if the market price of risk is unbounded. It is thus not straightforward to generalize results on continuous-time portfolio problems with power utility, Gaussian interest rates, and bounded market price of risk to situations where the short rate is Non-Gaussian or the market price of risk is unbounded.

Suggested Citation

  • Holger Kraft, 2009. "Optimal Portfolios With Stochastic Short Rate: Pitfalls When The Short Rate Is Non-Gaussian Or The Market Price Of Risk Is Unbounded," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 12(06), pages 767-796.
    • Handle: RePEc:wsi:ijtafx:v:12:y:2009:i:06:n:s0219024909005452
    DOI: 10.1142/S0219024909005452
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    Cited by:

    1. Maj-Britt Nordfang & Mogens Steffensen, 2017. "Portfolio Optimization and Mortgage Choice," JRFM, MDPI, vol. 10(1), pages 1-21, January.
    2. Morita, Hiroshi & Okimoto, Tatsuyoshi, 2021. "The interest rate determination when economic variables are partially observable," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 72(C).
    3. Xiaoxiao Zheng & Xin Zhang, 2014. "Optimal investment-reinsurance policy under a long-term perspective," Papers 1406.7604, arXiv.org.

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