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

Yan Wang; Yanxiang Zhao; Lei Wang; Aimin Song; Yanping Ma

doi:10.3934/jimo.2017067

Article Contents

2018, Volume 14, Issue 2: 653-671. Doi: 10.3934/jimo.2017067

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

Received: April 2016

Revised: December 2016

Early access: June 2017

Published: April 2018

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.).

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Abstract

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.

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Mathematics Subject Classification: Primary: 93E20, 60H30; Secondary: 91B30.

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