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Stochastic maximum principle for systems driven by local martingales with spatial parameters

The authors would like to thank Prof. Mingshang Hu for his helpful discussions. The authors are also grateful to the two anonymous referees for their valuable comments. J. Song is partially supported by Shandong University (Grant No. 11140089963041) and the National Natural Science Foundation of China (Grant No. 12071256).
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  • We consider the stochastic optimal control problem for the dynamical system of the stochastic differential equation driven by a local martingale with a spatial parameter. Assuming the convexity of the control domain, we obtain the stochastic maximum principle as the necessary condition for an optimal control, and we also prove its sufficiency under proper conditions. The stochastic linear quadratic problem in this setting is also discussed.

    Mathematics Subject Classification: 93E20, 60H10.


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