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A Dynamic Investment Model With Control On The Portfolio’S Worst Case Outcome

In: Selected Works of William T Ziemba A Memorial Volume

Author

Listed:
  • 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, 2024. "A Dynamic Investment Model With Control On The Portfolio’S Worst Case Outcome," World Scientific Book Chapters, in: Leonard MacLean & Sébastien Lleo (ed.), Selected Works of William T Ziemba A Memorial Volume, chapter 8, pages 123-143, World Scientific Publishing Co. Pte. Ltd..
    • Handle: RePEc:wsi:wschap:9789811285530_0008
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    More about this item

    Keywords

    William Ziemba; Financial Planning Models; Racetrack Betting; Sports Analytics; Market Anomalies; Risk Factors;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling

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