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Risk Budgeting Allocation for Dynamic Risk Measures

Author

Listed:
  • Silvana M. Pesenti

    (Department of Statistical Sciences, University of Toronto, Toronto, Ontario M5G 1Z5, Canada)

  • Sebastian Jaimungal

    (Department of Statistical Sciences, University of Toronto, Toronto, Ontario M5G 1Z5, Canada; and Oxford-Man Institute, University of Oxford, Oxford OX2 6ED, United Kingdom)

  • Yuri F. Saporito

    (School of Applied Mathematics, Getulio Vargas Foundation, Rio de Janeiro 22250-900, Brazil)

  • Rodrigo S. Targino

    (School of Applied Mathematics, Getulio Vargas Foundation, Rio de Janeiro 22250-900, Brazil)

Abstract

We define and develop an approach for risk budgeting allocation—a risk diversification portfolio strategy—where risk is measured using a dynamic time-consistent risk measure. For this, we introduce a notion of dynamic risk contributions that generalize the classical Euler contributions, which allows us to obtain dynamic risk contributions in a recursive manner. We prove that for the class of coherent dynamic distortion risk measures, the risk allocation problem may be recast as a sequence of strictly convex optimization problems. Moreover, we show that self-financing dynamic risk budgeting strategies with initial wealth of one are scaled versions of the solution of the sequence of convex optimization problems. Furthermore, we develop an actor-critic approach, leveraging the elicitability of dynamic risk measures, to solve for risk budgeting strategies using deep learning.

Suggested Citation

  • Silvana M. Pesenti & Sebastian Jaimungal & Yuri F. Saporito & Rodrigo S. Targino, 2025. "Risk Budgeting Allocation for Dynamic Risk Measures," Operations Research, INFORMS, vol. 73(3), pages 1208-1229, May.
    • Handle: RePEc:inm:oropre:v:73:y:2025:i:3:p:1208-1229
    DOI: 10.1287/opre.2023.0299
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