Discrete Error Estimates Of Stochastic Linear Quadratic Optimal Control Problems With Control Constraints

Stochastic linear quadratic optimal control problems with control constraints have important applications in engineering,finance.Solving such problems numerically has important theoretical and practical significance.One of the methods for solving the stochastic linear quadratic optimal control problems with control constraints is to discretize it by selecting an appropriate discrete scheme,and obtain the approximate solution of the optimal controls by solving the discretized stochastic programming problems.Therefore,it is very important to establish the discrete error estimates for optimal controls.In this thesis,we study discrete error estimates of stochastic linear quadratic optimal control problems with control constraints.The specific content includes: 1)when the diffusion term of the control system does not contain control,the stochastic linear quadratic optimal control problems are discretization by using the Euler difference scheme,and the discrete error estimates are established,to establish the discrete error estimation of optimal control,which allows control is random;2)we established a discrete error estimation for the optimal control in the case where the diffusion term includes control but allows control to be deterministic,where the allow control is independent of the sample points.The first order necessary condition of stochastic optimal controls and the estimates of the solutions to stochastic differential equations are two main tools for obtaining the discrete error estimates of optimal control problems.