Optimal Control of Conditional Value-at-Risk in Continuous Time

摘要: We consider continuous-time stochastic optimal control problems featuring Conditional Value-at-Risk (CVaR) in the objective. The major difficulty these arises from time-inconsistency, which prevents us directly using dynamic programming. To resolve this challenge, we convert to an equivalent bilevel optimization problem inner is standard control. Furthermore, provide conditions under outer objective function convex and differentiable. compute objective's value via a Hamilton-Jacobi-Bellman equation its gradient viscosity solution of linear parabolic equation, allows perform descent. significance result that efficient programming-based algorithm for CVaR without lifting state-space. broaden applicability proposed algorithm, propose convergent approximation schemes cases where our key assumptions do not hold characterize relevant suboptimality bounds. In addition, extend method more general class risk metrics, includes mean-variance median-deviation. also demonstrate concrete application portfolio constraints. Our results contribute framework solving time-inconsistent CVaR-based sequential optimization.