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SCIENCE CHINA Information Sciences, Volume 61, Issue 7: 070211(2018) https://doi.org/10.1007/s11432-017-9267-0

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

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  • ReceivedAug 25, 2017
  • AcceptedSep 28, 2017
  • PublishedMay 18, 2018

Abstract

In this article, we consider the partially observed optimal control problemfor 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 appliedto the motivating example of the risk minimization for portfolio selection.


Acknowledgment

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).


References

[1] Donnelly C. Sufficient stochastic maximum principle in a regime-switching diffusion model. Appl Math Optim, 2011, 64: 155-169 CrossRef Google Scholar

[2] Donnelly C, Heunis A J. Quadratic Risk Minimization in a Regime-Switching Model with Portfolio Constraints. SIAM J Control Optim, 2012, 50: 2431-2461 CrossRef Google Scholar

[3] Zhang X, Elliott R J, Siu T K. A stochastic maximum principle for a markov regime-switching jump-diffusion model and its application to finance. SIAM J Control Optim, 2012, 50: 964-990 CrossRef Google Scholar

[4] Zhang Q. Controlled partially observed diffusions with correlated noise. Appl Math Optim, 1990, 22: 265-285 CrossRef Google Scholar

[5] Xiong J, Zhou X Y. Mean?Variance Portfolio Selection under Partial Information. SIAM J Control Optim, 2007, 46: 156-175 CrossRef Google Scholar

[6] Tang S. The Maximum Principle for Partially Observed Optimal Control of Stochastic Differential Equations. SIAM J Control Optim, 1998, 36: 1596-1617 CrossRef Google Scholar

[7] Wang G C, Wu Z. The maximum principles for stochastic recursive optimal control problems under partial information. IEEE Trans Automat Contr, 2009, 54: 1230-1242 CrossRef Google Scholar

[8] Wang G C, Zhang C, Zhang W. Stochastic maximum principle for mean-field type optimal control under partial information. IEEE Trans Automat Contr, 2014, 59: 522-528 CrossRef Google Scholar

[9] Øksendal B, Sulem A. Maximum principles for optimal control of forward-backward stochastic differential equations with jumps. SIAM J Control Optim, 2009, 48: 2945--2976. Google Scholar

[10] Huang J, Wang G, Xiong J. A maximum principle for partial information backward stochastic control problems with applications. SIAM J Control Optim, 2009, 48: 2106-2117 CrossRef Google Scholar

[11] Wang G C, Wu Z, Xiong J. Maximum principles for forward-backward stochastic control systems with correlated state and observation noises. SIAM J Control Optim, 2013, 51: 491-524 CrossRef Google Scholar

[12] Wang G C, Wu Z, Xiong J. A linear-quadratic optimal control problem of forward-backward stochastic differential equations with partial information. IEEE Trans Automat Contr, 2015, 60: 2904-2916 CrossRef Google Scholar

[13] Wang G C, Wu Z. Kalman-Bucy filtering equations of forward and backward stochastic systems and applications to recursive optimal control problems. J Math Anal Appl, 2008, 342: 1280-1296 CrossRef ADS Google Scholar

[14] Wang G C, Wu Z. General Maximum Principles for Partially Observed Risk-Sensitive Optimal Control Problems and Applications to Finance. J Optim Theor Appl, 2009, 141: 677-700 CrossRef Google Scholar

[15] Wu Z. A maximum principle for partially observed optimal control of forward-backward stochastic control systems. Sci China Inf Sci, 2010, 53: 2205-2214 CrossRef Google Scholar

[16] Wang G C, Wu Z, Xiong J. An introduction to optimal control of FBSDE with incomplete information. In: SpringerBriefs in Mathematics. Berlin: Springer, 2018. Google Scholar

[17] Huang J, Zhang D. The near-optimal maximum principle of impulse control for stochastic recursive system. Sci China Inf Sci, 2016, 59: 112206 CrossRef Google Scholar

[18] Elliott R J, Aggoun L, Moore J B. Hidden Markov Models: Estimation and Control. New York: Springer, 1994. 176--182. Google Scholar

[19] Buckdahn R, Li J, Peng S. Mean-field backward stochastic differential equations and related partial differential equations. Stochastic Processes their Appl, 2009, 119: 3133-3154 CrossRef Google Scholar

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