A general maximum principle for progressive optimal stochastic control problems with Markov regime-switching
ESAIM: Control, Optimisation and Calculus of Variations, Tome 28 (2022), article no. 61

In this paper, we give a general maximum principle for optimal controls of stochastic systems driven by Markov chains. The control is allowed to enter both diffusion and jump terms and the control domain is not necessarily convex. We apply a new spike variation and the stochastic integral of progressive processes to obtain the main result.

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DOI : 10.1051/cocv/2022054
Classification : 60H10, 93E20
Keywords: The maximum principle, Markov chain, regime-switching, spike variation 
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     title = {A general maximum principle for progressive optimal stochastic control problems with {Markov} regime-switching},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     year = {2022},
     publisher = {EDP-Sciences},
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Song, Yuanzhuo; Wu, Zhen. A general maximum principle for progressive optimal stochastic control problems with Markov regime-switching. ESAIM: Control, Optimisation and Calculus of Variations, Tome 28 (2022), article no. 61. doi: 10.1051/cocv/2022054

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This work was supported by the Natural Science Foundation of China (11831010, 61961160732), Shandong Provincial Natural Science Foundation (ZR2019ZD42) and the Taishan Scholars Climbing Program of Shandong (No. TSPD20210302).