Acta mathematica scientia,Series A ›› 2021, Vol. 41 ›› Issue (2): 538-547.

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On Optimal Dividend and Reinsurance Problems in the Diffusion Risk Model with Random Time Horizon

Xiao Liu(),Peng Yao(),Zhenlong Chen*()   

  1. 1 School of Mathematics and Statistics, Anhui Normal University, Anhui Wuhu 241003
    2 School of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou 310018
  • Received:2020-04-27 Online:2021-04-26 Published:2021-04-29
  • Contact: Zhenlong Chen E-mail:yjjatyjjat@163.com;2845897419@qq.com;zlchenv@163.com
  • Supported by:
    the NSFC(11971432);the NSF of Anhui Province(1908085MA21);the Doctor Startup Funds of Anhui Normal University(2016XJJ119);the Humanities and Social Sciences Research Project of Ministry of Education(18YJA910001);the NSF of Zhejiang Province(LY21G010003)

Abstract:

This paper studies the optimal dividend and reinsurance problems in the diffusion risk model with random time horizon. Assume that the proportional reinsurance strategy is applied, the random time is exponentially distributed, and if the random time comes before ruin, a fixed nonnegative value exists, otherwise another fixed nonnegative value exists, the optimal dividend and reinsurance strategies and the explicit expressions of the value function are obtained, and a numerical example is presented.

Key words: Optimal dividends, Optimal reinsurance, Stochastic control

CLC Number: 

  • O212.62
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