Study of convergence rates of numerical methods for stochastic control problems

This work is concerned with convergence rates of numerical methods for stochastic control problems with a stopping time. We use Markov chain approximation techniques. Although the convergence rates may be studied by considering the convergence rates of finite difference schemes for Hamilton-Jacobi-Bellman (HJB) equations, in the current problem, there is an additional difficulty due to the boundary condition, which requires the continuity of the first exit time with respect to the discrete parameter. To prove the convergence of the algorithm by Markov chain approximation method, there might be a problem known as tangency problem. Convergence rate is achieved by boundary perturbation under certain assumption. Convergence rates of Markov chain approximation for certain controlled diffusion problems are verified.