The objective of this research is to use the notions and methods of non-smooth analysis to establish a new type of connection between optimal stochastic control problems and the Hamilton- Jacobi-Bellman equation irrespective of the possible degeneracy properties of the underlying processes. This would provide a new insight into the interrelation between variational problems and certain nonlinear partial differential equations as well as a unified approach to both deterministic and stochastic optimal control theory. The core of the research is the investigation of the regularity of properties of the optimal value function in terms of its subdifferentials, Clarke derivatives and the finding of a class of non-smooth functions in which the Hamilton-Jacobi- Bellman equation is uniquely solvable. Accumulation of computational and modeling experience on application problems are also parts of the project.
