Stochastic Optimal Control of Averaged SDDE with Semi-Markov Switching and with Application in Economics

Mariya Svishchuk and Anatoliy V. Swishchuk ()
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Mariya Svishchuk: Department of Mathematics and Computer Sciences, Mount Royal University, Calgary, AB T3E 6K6, Canada
Anatoliy V. Swishchuk: Department of Mathematics and Statistics, University of Calgary, Calgary, AB T2N 1N4, Canada

Mathematics, 2025, vol. 13, issue 9, 1-13

Abstract: 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.

Keywords: stochastic differential delay equations; stochastic optimal control; Hamilton–Jacobi–Bellman equation; Dynkin formula; Dirichlet–Poisson problem; economics applications; semi-Markov process; Ramsey economics model with delay and semi-Markov switching (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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