A Martingale approach to continuous Portfolio Optimization under CVaR like constraints
Optimization and Control
2025-10-01 v1 Statistics Theory
Risk Management
Statistics Theory
Abstract
We study a continuous-time portfolio optimization problem under an explicit constraint on the Deviation Conditional Value-at-Risk (DCVaR), defined as the difference between the CVaR and the expected terminal wealth. While the mean-CVaR framework has been widely explored, its time-inconsistency complicates the use of dynamic programming. We follow the martingale approach in a complete market setting, as in Gao et al. [4], and extend it by retaining an explicit DCVaR constraint in the problem formulation. The optimal terminal wealth is obtained by solving a convex constrained minimization problem. This leads to a tractable and interpretable characterization of the optimal strategy.
Cite
@article{arxiv.2509.26009,
title = {A Martingale approach to continuous Portfolio Optimization under CVaR like constraints},
author = {Jérôme Lelong and Véronique Maume-Deschamps and William Thevenot},
journal= {arXiv preprint arXiv:2509.26009},
year = {2025}
}