On a Periodic Capital Injection and Barrier Dividend Strategy in the Compound Poisson Risk Model

Wenguang Yu, Peng Guo, Qi Wang, Guofeng Guan, Qing Yang, Yujuan Huang, Xinliang Yu, Boyi Jin and Chaoran Cui
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Wenguang Yu: School of Insurance, Shandong University of Finance and Economics, Jinan 250014, China
Peng Guo: College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China
Qi Wang: School of Mathematic and Quantitative Economics, Shandong University of Finance and Economics, Jinan 250014, China
Guofeng Guan: School of Insurance, Shandong University of Finance and Economics, Jinan 250014, China
Qing Yang: School of Insurance, Shandong University of Finance and Economics, Jinan 250014, China
Yujuan Huang: School of Science, Shandong Jiaotong University, Jinan 250357, China
Xinliang Yu: School of Insurance, Shandong University of Finance and Economics, Jinan 250014, China
Boyi Jin: School of Insurance, Shandong University of Finance and Economics, Jinan 250014, China
Chaoran Cui: School of Computer Science & Technology, Shandong University of Finance and Economics, Jinan 250014, China

Mathematics, 2020, vol. 8, issue 4, 1-21

Abstract: In this paper, we assume that the reserve level of an insurance company can only be observed at discrete time points, then a new risk model is proposed by introducing a periodic capital injection strategy and a barrier dividend strategy into the classical risk model. We derive the equations and the boundary conditions satisfied by the Gerber-Shiu function, the expected discounted capital injection function and the expected discounted dividend function by assuming that the observation interval and claim amount are exponentially distributed, respectively. Numerical examples are also given to further analyze the influence of relevant parameters on the actuarial function of the risk model.

Keywords: compound Poisson risk model; periodic capital injection strategy; periodic barrier dividend strategy; Gerber-Shiu function; expected discounted dividend function; expected discounted capital injection function; characteristic equation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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