Multi periods mean-DCVaR optimization: a Recursive Neural Network resolution

J\'er\^ome Lelong, V\'eronique Maume-Deschamps and William Thevenot
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J\'er\^ome Lelong: LJK
V\'eronique Maume-Deschamps: ICJ, PSPM
William Thevenot: ICJ, PSPM

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Abstract: We study a discrete-time multi-period portfolio optimization problem under an explicit constraint on the Deviation Conditional Value-at-Risk (DCVaR), defined as the excess of Conditional Value-at-Risk over expected terminal wealth. The objective is to maximize expected return subject to a global tail-risk constraint, leading to a time-inconsistent precommitment problem. We propose a recurrent neural-network-based approach to approximate the optimal precommitment policy, which accommodates path-dependent risk constraints and highdimensional state dynamics without relying on dynamic programming. The explicit constraint formulation allows for exact penalty methods and provides a transparent notion of feasibility. The methodology is validated in a classical complete-market financial model and extended to a multi-period portfolio allocation problem in (re)insurance, capturing the long-term risk dynamics of insurance liabilities.

Date: 2026-04
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