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A dynamic programming approach to path-dependent constrained portfolios

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  • Marcos Escobar-Anel

    (University of Western Ontario)

Abstract

This paper introduces a methodology to produce analytical solutions to an expected utility optimization problem with path-dependent constraints on wealth. This is achieved via a combination of dynamic programming and financial derivatives. The paper focuses on solving the case of a Value at Risk constraint on the running minimum of the wealth process. The optimal wealth is shown to be a barrier-type contingent claim on the unconstrained optimal wealth; the optimal investment strategy and value function follow similarly. A comparison of Value at Risk constraints between terminal wealth and the running minimum of wealth demonstrates a difference of up to 30% on risky asset allocation. Other meaningful examples of interest for investment managers are briefly described.

Suggested Citation

  • Marcos Escobar-Anel, 2022. "A dynamic programming approach to path-dependent constrained portfolios," Annals of Operations Research, Springer, vol. 315(1), pages 141-157, August.
    • Handle: RePEc:spr:annopr:v:315:y:2022:i:1:d:10.1007_s10479-022-04640-4
    DOI: 10.1007/s10479-022-04640-4
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    References listed on IDEAS

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