# American Institute of Mathematical Sciences

April  2018, 14(2): 653-671. doi: 10.3934/jimo.2017067

## Stochastic maximum principle for partial information optimal investment and dividend problem of an insurer

 1 School of Science, Dalian Jiaotong University, Dalian 116028, China 2 Department of Mathematics, The George Washington University, Washington DC 20052, USA 3 School of Mathematical Sciences, Dalian University of Technology, Dalian 116023, China 4 Department of Mathematics, Loyola Marymount University, Los Angeles CA 90045, USA

* Corresponding author. E-mail address: wanglei@dlut.edu.cn

The reviewing process was handled by Changjun Yu

Received  April 2016 Revised  December 2016 Published  June 2017

Fund Project: 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), the Research Funding for Doctor Start-Up Program of Liaoning Province (Grant 201601245), the Fundamental Research Funds for Central Universities in China (Grant DUT15LK25), the Simons Foundation through Grant No. 357963 (Y.Z.), a start-up grant from the George Washington University (Y.Z.), Loyola Marymount University CSE continuing Faculty Research grant (Y.M.), and a start-up grant from Loyola Marymount University (Y.M.).

We study an optimal investment and dividend problem of an insurer, where the aggregate insurance claims process is modeled by a pure jump Lévy process. We allow the management of the dividend payment policy and the investment of surplus in a continuous-time financial market, which is composed of a risk free asset and a risky asset. The information available to the insurer is partial information. We generalize this problem as a partial information regular-singular stochastic control problem, where the control variable consists of regular control and singular control. Then maximum principles are established to give sufficient and necessary optimality conditions for the solutions of the regular-singular control problem. Finally we apply the maximum principles to solve the investment and dividend problem of an insurer.

Citation: Yan Wang, Yanxiang Zhao, Lei Wang, Aimin Song, Yanping Ma. Stochastic maximum principle for partial information optimal investment and dividend problem of an insurer. Journal of Industrial & Management Optimization, 2018, 14 (2) : 653-671. doi: 10.3934/jimo.2017067
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