J Anal https://doi.org/10.1007/s41478-018-0098-1 ORIGINAL RESEARCH PAPER Infinite horizon optimal control of mean‑field delay system with semi‑Markov modulated jump‑diffusion processes 1 1 R. Deepa · P. Muthukumar Received: 16 November 2017 / Accepted: 18 May 2018 © Forum D’Analystes, Chennai 2018 Abstract This paper describes the study of infinite horizon optimal control of sto - chastic delay differential equation with semi-Markov modulated jump-diffusion pro - cesses in which the control domain is not convex. In addition, the drift, diffusion, jump kernel term and cost functional are modulated by semi-Markov processes and expectation values of the state processes. Since the control domain is non-convex, the system exhibits non-guarantee to exist optimal control. Therefore, the concerned system is transformed into relaxed control model where the set of all relaxed con- trols forms a convex set, which gives the existence of optimal control. Further, sto- chastic maximum principle and necessary condition for optimality are established under convex perturbation technique for the relaxed model. Finally, an application of the theoretical study is shown by an example of portfolio optimization problem in financial market. Keywords Infinite-horizon · Mean field optimal control · Relaxed control · Semi- Markov modulated jump-diffusion processes · Stochastic maximum principle Mathematics Subject Classification 35B50 · 60H10 · 93E20. This work was
The Journal of Analysis – Springer Journals
Published: Jun 4, 2018
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