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An Optimal Control Problem in a Risk Model with Stochastic Premiums and Periodic Dividend Payments

Xixi Yang

School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, P. R. China

E-mail Address: 836921399@qq.com

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Jiyang Tan

School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, P. R. China

E-mail Address: tanjiyang15@163.com

Corresponding author.

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Hanjun Zhang

School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, P. R. China

E-mail Address: hjz001@xtu.edu.cn

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, and

Ziqiang Li

School of Information Engineering, Xiangtan University, Xiangtan 411105, P. R. China

E-mail Address: xtulzq@hotmail.com

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https://doi.org/10.1142/S0217595917400139Cited by:5 (Source: Crossref)

Abstract

In this paper, a discrete-time risk model is considered. We assume that the premium received in each time interval is a positive real-valued random variable, and the sequence of premiums is a Markov chain. In any time interval the probability of a claim occurrence is related to the premium received in the corresponding period. We discuss control strategies for dividends paid periodically to the shareholders under two cases: absence and presence of ceiling restriction for dividend rates. We provide algorithms and some properties for the optimal control strategies by transforming the value function.

Keywords:

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