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Utility maximization under a shortfall risk constraint

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  • Gundel, Anne
  • Weber, Stefan
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    Abstract

    The article analyzes optimal portfolio choice of utility maximizing agents in a general continuous-time financial market model under a joint budget and downside risk constraint. The risk constraint is given in terms of a class of convex risk measures. We do not impose any specific assumptions on the price processes of the underlying assets. We analyze under which circumstances the risk constraint is binding. We provide a closed-form solution to the optimization problem in a general semimartingale framework. For a complete market, the wealth maximization problem is equivalent to a dynamic portfolio optimization problem.

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    File URL: http://www.sciencedirect.com/science/article/B6VBY-4RRNXSX-2/2/f9e2ad33dc48cd79dc1823bee8e62e62
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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Mathematical Economics.

    Volume (Year): 44 (2008)
    Issue (Month): 11 (December)
    Pages: 1126-1151

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    Handle: RePEc:eee:mateco:v:44:y:2008:i:11:p:1126-1151

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    Web page: http://www.elsevier.com/locate/jmateco

    Related research

    Keywords: Utility maximization Optimal portfolio choice Utility-based shortfall risk Convex risk measures Semimartingales;

    References

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    1. Hua He and Neil D. Pearson., 1989. "Consumption and Portfolio Policies with Incomplete Markets and Short-Sale Constraints: The Infinite Dimensional Case," Research Program in Finance Working Papers RPF-191, University of California at Berkeley.
    2. Schied Alexander & Wu Ching-Tang, 2005. "Duality theory for optimal investments under model uncertainty," Statistics & Risk Modeling, De Gruyter, vol. 23(3/2005), pages 199-217, March.
    3. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    4. Alexander Schied & Ching-Tang Wu, 2005. "Duality theory for optimal investments under model uncertainty," SFB 649 Discussion Papers SFB649DP2005-025, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany, revised Sep 2005.
    5. Riedel, Frank & Bank, Peter, 1998. "Non-time additive utility optimization: The case of certainty," SFB 373 Discussion Papers 1998,108, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    6. Thomas Goll & Ludger Rüschendorf, 2001. "Minimax and minimal distance martingale measures and their relationship to portfolio optimization," Finance and Stochastics, Springer, vol. 5(4), pages 557-581.
    7. 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.
    8. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
    9. Basak, Suleyman & Shapiro, Alexander, 2001. "Value-at-Risk-Based Risk Management: Optimal Policies and Asset Prices," Review of Financial Studies, Society for Financial Studies, vol. 14(2), pages 371-405.
    10. Anne Gundel, 2005. "Robust utility maximization for complete and incomplete market models," Finance and Stochastics, Springer, vol. 9(2), pages 151-176, 04.
    11. Cox, John C. & Huang, Chi-fu, 1989. "Optimal consumption and portfolio policies when asset prices follow a diffusion process," Journal of Economic Theory, Elsevier, vol. 49(1), pages 33-83, October.
    12. Gundel, Anne & Weber, Stefan, 2007. "Robust utility maximization with limited downside risk in incomplete markets," Stochastic Processes and their Applications, Elsevier, vol. 117(11), pages 1663-1688, November.
    13. Stefan Weber, 2006. "Distribution-Invariant Risk Measures, Information, And Dynamic Consistency," Mathematical Finance, Wiley Blackwell, vol. 16(2), pages 419-441.
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