A Dynamic Investment Model with Control on the Portfolio's Worst Case Outcome |
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| Authors: | Yonggan Zhao Ulrich Haussmann William T Ziemba |
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| Institution: | Nanyang Business School, Nanyang Technological University, Singapore;, Department of Mathematics, University of British Columbia;, Sauder School of Business, University of British Columbia |
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| 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. |
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| Keywords: | portfolio selection martingale option worst case outcome downside risk control |
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