2023/06/22 by Gabriel Velho, Jean Auriol, Velho, Gabriel +3 · 1 citation
Decision Sciences · Economics, Econometrics and Finance · Social Sciences · #FOS: Mathematics #Insurance, Mortality, Demography, Risk Management #Optimization and Control (math.OC) #Risk and Portfolio Optimization #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2306.12878
openalex publication_date 2023/06/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we consider continuous-time stochastic optimal control problems where the cost is evaluated through a coherent risk measure. We provide an explicit gradient descent-ascent algorithm which applies to problems subject to non-linear stochastic differential equations. More specifically, we leverage duality properties of coherent risk measures to relax the problem via a smooth min-max reformulation which induces artificial strong concavity in the max subproblem. We then formulate necessary conditions of optimality for this relaxed problem which we leverage to prove convergence of the gradient descent-ascent algorithm to candidate solutions of the original problem. Finally, we showcase the efficiency of our algorithm through numerical simulations involving trajectory tracking problems and highlight the benefit of favoring risk measures over classical expectation.