A Martingale approach to continuous Portfolio Optimization under CVaR like constraints

Paper: arXiv 2509.26009

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

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.

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 3.0/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a rigorous mathematical theoretical framework for portfolio optimization under continuous time using the martingale method and DCVaR constraints. However, it lacks extensive empirical backtesting and relies heavily on ideal assumptions like market completeness.

Research Flowchart

  flowchart TD
    A[Research Goal: Portfolio Optimization under DCVaR Constraint in Continuous Time] --> B[Inputs: Market Parameters & Risk Tolerance Thresholds]
    B --> C[Methodology: Apply Martingale Approach in Complete Market Setting]
    C --> D[Formulate & Solve Convex Constrained Minimization Problem]
    D --> E[Derive Explicit Characterization of Optimal Terminal Wealth]
    E --> F[Outcomes: Tractable & Interpretable Dynamic Strategy Resolving Time-Inconsistency]