Stochastic Optimal Control of Averaged SDDE with Semi-Markov Switching and with Application in Economics
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) e...
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2025-04-01
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| author | Mariya Svishchuk Anatoliy V. Swishchuk |
| author_facet | Mariya Svishchuk Anatoliy V. Swishchuk |
| author_sort | Mariya Svishchuk |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-be8fbd7fe3b64cc08061b37c4850b602 |
| institution | DOAJ |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-be8fbd7fe3b64cc08061b37c4850b6022025-08-20T02:58:44ZengMDPI AGMathematics2227-73902025-04-01139144010.3390/math13091440Stochastic Optimal Control of Averaged SDDE with Semi-Markov Switching and with Application in EconomicsMariya Svishchuk0Anatoliy V. Swishchuk1Department of Mathematics and Computer Sciences, Mount Royal University, Calgary, AB T3E 6K6, CanadaDepartment of Mathematics and Statistics, University of Calgary, Calgary, AB T2N 1N4, CanadaThis 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.https://www.mdpi.com/2227-7390/13/9/1440stochastic differential delay equationsstochastic optimal controlHamilton–Jacobi–Bellman equationDynkin formulaDirichlet–Poisson problemeconomics applications |
| spellingShingle | Mariya Svishchuk Anatoliy V. Swishchuk Stochastic Optimal Control of Averaged SDDE with Semi-Markov Switching and with Application in Economics Mathematics stochastic differential delay equations stochastic optimal control Hamilton–Jacobi–Bellman equation Dynkin formula Dirichlet–Poisson problem economics applications |
| title | Stochastic Optimal Control of Averaged SDDE with Semi-Markov Switching and with Application in Economics |
| title_full | Stochastic Optimal Control of Averaged SDDE with Semi-Markov Switching and with Application in Economics |
| title_fullStr | Stochastic Optimal Control of Averaged SDDE with Semi-Markov Switching and with Application in Economics |
| title_full_unstemmed | Stochastic Optimal Control of Averaged SDDE with Semi-Markov Switching and with Application in Economics |
| title_short | Stochastic Optimal Control of Averaged SDDE with Semi-Markov Switching and with Application in Economics |
| title_sort | stochastic optimal control of averaged sdde with semi markov switching and with application in economics |
| topic | stochastic differential delay equations stochastic optimal control Hamilton–Jacobi–Bellman equation Dynkin formula Dirichlet–Poisson problem economics applications |
| url | https://www.mdpi.com/2227-7390/13/9/1440 |
| work_keys_str_mv | AT mariyasvishchuk stochasticoptimalcontrolofaveragedsddewithsemimarkovswitchingandwithapplicationineconomics AT anatoliyvswishchuk stochasticoptimalcontrolofaveragedsddewithsemimarkovswitchingandwithapplicationineconomics |