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Maximum principle via Malliavin calculus for regular-singular stochastic differential games

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Abstract

We consider non-zero-sum regular-singular stochastic differential games, where the informations available to the two players are asymmetry partial informations. The control strategy of each player consists of two components: regular control and singular control. Applying the Malliavin calculus approach, we establish a necessary maximum principle for the games, where the adjoint processes are explicitly represented by the parameters and the states of the system.

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Acknowledgements

This work was supported by The National Natural Science Foundation for the Youth of China (Grants 11301081, 11401073), The Science Research Project of Educational Department of Liaoning Province of China (Grants L2014188, L2015097 and L2014186), and The Fundamental Research Funds for Central Universities in China (Grant DUT15LK25).

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Authors and Affiliations

  1. School of Science, Dalian Jiaotong University, Dalian, 116028, China

    Yan Wang & Aimin Song

  2. School of Mathematical Sciences, Dalian University of Technology, Dalian, 116023, China

    Lei Wang

  3. Department of Mathematics and Statistics, Curtin University, Bentley, Australia

    Jie Sun

Authors
  1. Yan Wang
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  2. Aimin Song
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  3. Lei Wang
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  4. Jie Sun
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Correspondence to Aimin Song.

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Wang, Y., Song, A., Wang, L. et al. Maximum principle via Malliavin calculus for regular-singular stochastic differential games. Optim Lett 12, 1301–1314 (2018). https://doi.org/10.1007/s11590-017-1120-2

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  • DOI: https://doi.org/10.1007/s11590-017-1120-2

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