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A Dynamic Investment Model with Control on the Portfolio's Worst Case Outcome

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  • Yonggan Zhao
  • Ulrich Haussmann
  • William T. Ziemba

Abstract

This paper considers a portfolio problem with control on downside losses. Incorporating the worst‐case portfolio outcome in the objective function, the optimal policy is equivalent to the hedging portfolio of a European option on a dynamic mutual fund that can be replicated by market primary assets. Applying the Black‐Scholes formula, a closed‐form solution is obtained when the utility function is HARA and asset prices follow a multivariate geometric Brownian motion. The analysis provides a useful method of converting an investment problem to an option pricing model.

Suggested Citation

  • Yonggan Zhao & Ulrich Haussmann & William T. Ziemba, 2003. "A Dynamic Investment Model with Control on the Portfolio's Worst Case Outcome," Mathematical Finance, Wiley Blackwell, vol. 13(4), pages 481-501, October.
    • Handle: RePEc:bla:mathfi:v:13:y:2003:i:4:p:481-501
    DOI: 10.1111/1467-9965.t01-1-00177
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    Cited by:

    1. Leitner Johannes, 2005. "Optimal portfolios with expected loss constraints and shortfall risk optimal martingale measures," Statistics & Risk Modeling, De Gruyter, vol. 23(1/2005), pages 49-66, January.
    2. Kozhan, Roman & Schmid, Wolfgang, 2009. "Asset allocation with distorted beliefs and transaction costs," European Journal of Operational Research, Elsevier, vol. 194(1), pages 236-249, April.
    3. Kozhan, Roman & Salmon, Mark, 2009. "Uncertainty aversion in a heterogeneous agent model of foreign exchange rate formation," Journal of Economic Dynamics and Control, Elsevier, vol. 33(5), pages 1106-1122, May.
    4. Zhao, Yonggan & Ziemba, William T., 2008. "Calculating risk neutral probabilities and optimal portfolio policies in a dynamic investment model with downside risk control," European Journal of Operational Research, Elsevier, vol. 185(3), pages 1525-1540, March.

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