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Infinite horizon optimal control of mean-field delay system with semi-Markov modulated jump-diffusion processes

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Abstract

This paper describes the study of infinite horizon optimal control of stochastic delay differential equation with semi-Markov modulated jump-diffusion processes 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 controls forms a convex set, which gives the existence of optimal control. Further, stochastic 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.

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Acknowledgements

The author would like to thank the editor, the associate editor, and anonymous referees for their constructive corrections and valuable suggestions that improved the manuscript.

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Authors and Affiliations

  1. Department of Mathematics, The Gandhigram Rural Institute (Deemed to be University), Gandhigram, Tamilnadu, 624 302, India

    R. Deepa & P. Muthukumar

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  1. R. Deepa
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  2. P. Muthukumar
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Correspondence to R. Deepa.

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The authors declare that they have no conflict of interest.

Additional information

This work was supported by Science Engineering Research Board (SERB), DST, Govt. of India under YSS Project F.No: YSS/2014/000447 dated 20.11.2015. The first author is thankful to UGC, New Delhi for providing BSR fellowship for the year 2015.

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Deepa, R., Muthukumar, P. Infinite horizon optimal control of mean-field delay system with semi-Markov modulated jump-diffusion processes. J Anal 27, 623–641 (2019). https://doi.org/10.1007/s41478-018-0098-1

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  • DOI: https://doi.org/10.1007/s41478-018-0098-1

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