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Optimal portfolio strategies benchmarking the stock market

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  • A. Gabih
  • W. Grecksch
  • M. Richter
  • R. Wunderlich

Abstract

The paper investigates the impact of adding a shortfall risk constraint to the problem of a portfolio manager who wishes to maximize his utility from the portfolios terminal wealth. Since portfolio managers are often evaluated relative to benchmarks which depend on the stock market we capture risk management considerations by allowing a prespecified risk of falling short such a benchmark. This risk is measured by the expected loss in utility. Using the Black–Scholes model of a complete financial market and applying martingale methods, explicit analytic expressions for the optimal terminal wealth and the optimal portfolio strategies are given. Numerical examples illustrate the analytic results. Copyright Springer-Verlag 2006

Suggested Citation

  • A. Gabih & W. Grecksch & M. Richter & R. Wunderlich, 2006. "Optimal portfolio strategies benchmarking the stock market," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 64(2), pages 211-225, October.
    • Handle: RePEc:spr:mathme:v:64:y:2006:i:2:p:211-225
    DOI: 10.1007/s00186-006-0091-3
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    References listed on IDEAS

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    1. Basak, Suleyman & Shapiro, Alexander, 2001. "Value-at-Risk-Based Risk Management: Optimal Policies and Asset Prices," The Review of Financial Studies, Society for Financial Studies, vol. 14(2), pages 371-405.
    2. 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.
    3. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    4. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    5. 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.
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    Cited by:

    1. Frank Seifried, 2010. "Optimal investment with deferred capital gains taxes," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 71(1), pages 181-199, February.
    2. Jörn Sass & Ralf Wunderlich, 2010. "Optimal portfolio policies under bounded expected loss and partial information," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 72(1), pages 25-61, August.

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