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Worst Case Portfolio Optimization and HJB-Systems

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Author Info
Ralf Korn (Fachbereich Mathematik, Universität Kaiserslautern)
Mogens Steffensen (Department of Applied Mathematics and Statistics, University of Copenhagen)
Abstract

We formulate a portfolio optimization problem as a game where the investor chooses a portfolio and his opponent, the market, chooses some market crashes. The asymmetry of the opponents' decision processes leads to a new and delicate generalization of the classical Hamilton-Jacob-Bellman equation in stochastic control. We characterize the optimal controls in general and specify them further in the cases of HARA, logarithmic, and exponential utility of the investor.

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Paper provided by University of Copenhagen. Department of Economics. Finance Research Unit in its series FRU Working Papers with number 2006/02.

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Length: 16 pages
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Handle: RePEc:kud:kuiefr:200602

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Keywords: continuous-time game asymmetric decisions market crash utility optimization

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Browne, S., 1995. "Optimal Investment Policies for a Firm with a Random Risk Process: Exponential Utility and Minimizing the Probability of Ruin," Papers 95-08, Columbia - Graduate School of Business.
  2. Korn, Ralf, 2005. "Worst-case scenario investment for insurers," Insurance: Mathematics and Economics, Elsevier, vol. 36(1), pages 1-11, February. [Downloadable!] (restricted)
  3. Denis Talay & Ziyu Zheng, 2002. "Worst case model risk management," Finance and Stochastics, Springer, vol. 6(4), pages 517-537. [Downloadable!] (restricted)
  4. 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 247-57, August. [Downloadable!] (restricted)
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This page was last updated on 2008-9-29.

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