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

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.