A Martingale approach to continuous Portfolio Optimization under CVaR like constraints

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

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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.

Date: 2025-09
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