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Maximum Principle for Markov Regime-Switching Forward–Backward Stochastic Control System with Jumps and Relation to Dynamic Programming

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Abstract

This paper presents a sufficient stochastic maximum principle for a stochastic optimal control problem of Markov regime-switching forward–backward stochastic differential equations with jumps. The relationship between the stochastic maximum principle and the dynamic programming principle in a Markovian case is also established. Finally, applications of the main results to a recursive utility portfolio optimization problem in a financial market are discussed.

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Acknowledgements

The authors would like to thank the referees for their careful reading of the paper and helpful suggestions. This work is supported by the National Natural Science Foundation of China (NSFC Grant Nos. 11571189, 11371020) and the European Union’s Seventh Framework Programme for research, technological development and demonstration under Grant Agreement No. 318984-RARE.

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Correspondence to Junyi Guo.

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Communicated by Christiane Tammer.

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Sun, Z., Guo, J. & Zhang, X. Maximum Principle for Markov Regime-Switching Forward–Backward Stochastic Control System with Jumps and Relation to Dynamic Programming. J Optim Theory Appl 176, 319–350 (2018). https://doi.org/10.1007/s10957-017-1068-5

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  • DOI: https://doi.org/10.1007/s10957-017-1068-5

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