Optimal Control of CVaR Risk Measure in Continuous-Time using Radial Basis Function Collocation Method

In this paper, we consider continuous-time stochastic optimal control problems containing conditional value-at-risk (CVaR) in their objective function. The major di culty arising from these problems is the time inconsistency. To resolve this issue and based on [C. W. Miller and I. Yang, Optimal control of Conditional Value-at-Risk in continuous time, SIAM Journal on Control and Optimization 55.2 (2017): 856-884.], we convert the original formulation into an equivalent bi-level optimization problem. Based on the fact that inner optimization is a standard stochastic control problem, we numerically solve it by a radial basis function collocation method and demonstrate its effectiveness on a concrete application from portfolio optimization under CVaR constraints. We show the convergence of this approximation to the true optimal solution present some numerical experiments concerning computation of the effcient frontier.