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The importance of dynamic risk constraints for limited liability operators

Author

Listed:
  • John Armstrong

    (King’s College London)

  • Damiano Brigo

    (Imperial College London)

  • Alex S. L. Tse

    (University College London)

Abstract

Previous literature shows that prevalent risk measures such as value at risk or expected shortfall are ineffective to curb excessive risk-taking by a tail-risk-seeking trader with S-shaped utility function in the context of portfolio optimisation. However, these conclusions hold only when the constraints are static in the sense that the risk measure is just applied to the terminal portfolio value. In this paper, we consider a portfolio optimisation problem featuring S-shaped utility and a dynamic risk constraint which is imposed throughout the entire trading horizon. Provided that the risk control policy is sufficiently strict relative to the Sharpe ratio of the asset, the trader’s portfolio strategies and the resulting maximal expected utility can be effectively constrained by a dynamic risk measure. Finally, we argue that dynamic risk constraints might still be ineffective if the trader has access to a derivatives market.

Suggested Citation

  • John Armstrong & Damiano Brigo & Alex S. L. Tse, 2024. "The importance of dynamic risk constraints for limited liability operators," Annals of Operations Research, Springer, vol. 336(1), pages 861-898, May.
    • Handle: RePEc:spr:annopr:v:336:y:2024:i:1:d:10.1007_s10479-023-05295-5
    DOI: 10.1007/s10479-023-05295-5
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    More about this item

    Keywords

    Dynamic risk constraints; Limited liability operators; S-shaped utility; Portfolio optimisation;
    All these keywords.

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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