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

Author

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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)

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.

Suggested Citation

  • Mariya Svishchuk & Anatoliy V. Swishchuk, 2025. "Stochastic Optimal Control of Averaged SDDE with Semi-Markov Switching and with Application in Economics," Mathematics, MDPI, vol. 13(9), pages 1-13, April.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:9:p:1440-:d:1644403
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    References listed on IDEAS

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    2. Olivier Jean Blanchard & Stanley Fischer, 1989. "Lectures on Macroeconomics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262022834, December.
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