A DYNAMIC INVESTMENT MODEL WITH CONTROL ON THE PORTFOLIO’S WORST CASE OUTCOME

Yonggan Zhao, Ulrich Haussmann and William T. Ziemba

Chapter 8 in Selected Works of William T Ziemba:A Memorial Volume, 2024, pp 123-143 from World Scientific Publishing Co. Pte. Ltd.

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.

Keywords: William Ziemba; Financial Planning Models; Racetrack Betting; Sports Analytics; Market Anomalies; Risk Factors (search for similar items in EconPapers)
JEL-codes: C44 C6 G11 G12 (search for similar items in EconPapers)
Date: 2024
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