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

Paper: arXiv 2604.14439

Authors: Jérôme Lelong, Véronique Maume-Deschamps, William Thevenot

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.

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 6.0/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper tackles a complex, time-inconsistent multi-period optimization problem using a novel Recurrent Neural Network architecture to handle path-dependent DCVaR constraints. While mathematically rigorous with a solid framework for high-dimensional state dynamics, the empirical section relies heavily on synthetic/model-driven validation rather than extensive historical market backtesting.

Research Flowchart

  flowchart TD
    A[Research Goal: Multi-Period Portfolio Optimization<br/>with DCVaR Tail-Risk Constraint] --> B[Input Data: Financial Assets &<br/>Reinsurance Liabilities Dynamics]
    B --> C[Problem Formulation: Time-Inconsistent<br/>Precommitment Model + Exact Penalty]
    C --> D[RNN Optimization: Approximating Policy<br/>for Path-Dependent Risk]
    D --> E[Key Outcomes: Scalable Solution for<br/>High-Dim Portfolios & Long-Term Liabilities]