Viscosity Solutions of Stochastic Hamilton-Jacobi-Bellman Equations

Fully nonlinear stochastic Hamilton-Jacobi-Bellman (HJB) equations will be discussed for the optimal stochastic control problem of stochastic differential equations with random coefficients. The notion of viscosity solution is introduced, and the value function of the optimal stochastic control problem is the unique viscosity solution to the associated stochastic HJB equation. Applications and some recent developments will be reported as well.