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

Yonggan Zhao (), Ulrich Haussmann and William T. Ziemba

Mathematical Finance, 2003, vol. 13, issue 4, 481-501

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.

Date: 2003
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