A local iterative approach for solving the stochastic Hamilton‐Jacobi‐Bellman equation (SHJBE) arising in the stochastic control of affine nonlinear systems

Summary In this paper, local iterative methods for solving the stochastic Hamilton‐Jacobi‐Bellman equation arising in the stochastic optimal control of affine nonlinear systems are discussed. Superquadratic and quadratic convergence of the methods is established under fairly mild assumptions, and an example is solved to demonstrate the effectiveness of the methods. Finally, as a by‐product, an existence result for the solution to the stochastic Hamilton‐Jacobi‐Bellman equation is also established under the same assumptions.