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Stochastic maximum principle for partially observed forward-backward stochastic differential equations with jumps and regime switching

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Abstract

In this article, we consider the partially observed optimal control problem for forward-backward stochastic systems with Markovian regime switching. A stochastic maximum principle for optimal control is developed using a variational method and filtering technique. Our theoretical results are applied to the motivating example of the risk minimization for portfolio selection.

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Acknowledgements

ZHANG’s research was supported in part by National Natural Science Foundation of China (Grant Nos. 11501129, 71571053, 71771058) and Natural Science Foundation of Hebei Province (Grant No. A2014202202). XIONG’s research was supported by Macao Science and Technology Fund FDCT (Grant No. FDCT025/2016/A1).

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Correspondence to Shuaiqi Zhang.

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Zhang, S., Xiong, J. & Liu, X. Stochastic maximum principle for partially observed forward-backward stochastic differential equations with jumps and regime switching. Sci. China Inf. Sci. 61, 70211 (2018). https://doi.org/10.1007/s11432-017-9267-0

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Keywords

  • partial information
  • Markovian regime-switching
  • stochastic maximum principle
  • forward-backward stochastic differential equation (FBSDE)