Optimal Control of Vector Delayed RDS with Applications in Finance and Economics

This chapter is devoted to the study of RDS arising in optimal control theory for vector stochastic differential delay equations (SDDEs) and its applications in mathematical finance and economics. By using the Dynkin formula and solution of the Dirichlet-Poisson problem, the Hamilton-Jacobi-Bellman (HJB) equation and the converse HJB equation are derived. Furthermore, applications are given to an optimal portfolio selection problem and a stochastic Ramsey model in economics.