Risk Budgeting Allocation for Dynamic Risk Measures

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.

Funding: S. M. Pesenti and S. Jaimungal acknowledge support from the Natural Sciences and Engineering Research Council of Canada [Grants DGECR-2020-00333, RGPIN-2020-04289, RGPIN-2024-04317, RGPIN-2018-05705, and RGPAS-2018-522715]. Y. F. Saporito acknowledges support from the Conselho Nacional de Desenvolvimento Científico e Tecnológico [Grant 306695/2021-9] and the Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro [Grant E-26/201.375/2022 272760]. R. S. Targinoc acknowledges support from the Conselho Nacional de Desenvolvimento Científico e Tecnológico [Grant 200293/2022-2] and the Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro [Grants E-26/201.350, E-26/211.426, and E-26/211.578].