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

Jérôme Lelong (), Véronique Maume-Deschamps () and William Thevenot ()
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Jérôme Lelong: DAO - Données, Apprentissage et Optimisation - LJK - Laboratoire Jean Kuntzmann - Inria - Institut National de Recherche en Informatique et en Automatique - CNRS - Centre National de la Recherche Scientifique - UGA - Université Grenoble Alpes - Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology - UGA - Université Grenoble Alpes
Véronique Maume-Deschamps: ICJ - Institut Camille Jordan - ECL - École Centrale de Lyon - Université de Lyon - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon - INSA Lyon - Institut National des Sciences Appliquées de Lyon - Université de Lyon - INSA - Institut National des Sciences Appliquées - UJM - Université Jean Monnet - Saint-Étienne - UJM EPE - Université Jean Monnet (EPSCPE) - CNRS - Centre National de la Recherche Scientifique, PSPM - Probabilités, statistique, physique mathématique - ICJ - Institut Camille Jordan - ECL - École Centrale de Lyon - Université de Lyon - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon - INSA Lyon - Institut National des Sciences Appliquées de Lyon - Université de Lyon - INSA - Institut National des Sciences Appliquées - UJM - Université Jean Monnet - Saint-Étienne - UJM EPE - Université Jean Monnet (EPSCPE) - CNRS - Centre National de la Recherche Scientifique
William Thevenot: ICJ - Institut Camille Jordan - ECL - École Centrale de Lyon - Université de Lyon - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon - INSA Lyon - Institut National des Sciences Appliquées de Lyon - Université de Lyon - INSA - Institut National des Sciences Appliquées - UJM - Université Jean Monnet - Saint-Étienne - UJM EPE - Université Jean Monnet (EPSCPE) - CNRS - Centre National de la Recherche Scientifique, PSPM - Probabilités, statistique, physique mathématique - ICJ - Institut Camille Jordan - ECL - École Centrale de Lyon - Université de Lyon - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon - INSA Lyon - Institut National des Sciences Appliquées de Lyon - Université de Lyon - INSA - Institut National des Sciences Appliquées - UJM - Université Jean Monnet - Saint-Étienne - UJM EPE - Université Jean Monnet (EPSCPE) - CNRS - Centre National de la Recherche Scientifique

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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.

Keywords: Portfolio optimization; Conditional Value-at-Risk (CVaR); Deviation risk measures; Mean-risk optimization; Neural networks (search for similar items in EconPapers)
Date: 2026-04-09
Note: View the original document on HAL open archive server: https://hal.science/hal-05586106v1
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