Stochastic Optimal Control of Averaged SDDE with Semi-Markov Switching and with Application in Economics - Mariya Svishchuk; Anatoliy V. Swishchuk (Mathematics)
This paper is devoted to the study of stochastic optimal control of averaged stochastic differential delay equations (SDDEs) with semi-Markov switchings and their applications in economics. By using the Dynkin formula and solution of the Dirichlet–Poisson problem, the Hamilton–Jacobi–Bellman (HJB) equation and the inverse HJB equation are derived. Applications are given to a new Ramsey stochastic models in economics, namely the averaged Ramsey diffusion model with semi-Markov switchings. A numerical example is presented as well.