Randomized observation periods for compound Poisson risk model with capital injection and barrier dividend

Advances in Difference Equations

article

Yu, Wenguang¹  Guo, Peng²  Wang, Qi³  Guan, Guofeng³  Huang, Yujuan⁴  Yu, Xinliang¹ 

[1] School of Insurance, Shandong University of Finance and Economics;College of Mathematics and Statistics, Chongqing University;School of Mathematic and Quantitative Economics, Shandong University of Finance and Economics;School of Science, Shandong Jiaotong University

关键词: Compound Poisson risk model;    Capital injection;    Barrier dividend strategy;    Gerber–Shiu function;    The expected discounted capital injection;    The expected discounted dividend payments;    Randomized observation;    Laplace transform;   

DOI  :  10.1186/s13662-021-03378-w

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

In this paper, we model the insurance company’s surplus by a compound Poisson risk model, where the surplus process can only be observed at random observation times. It is assumed that the insurer observes its surplus level periodically to decide on dividend payments and capital injection at the interobservation time having an$\operatorname{Erlang}(n)$ distribution. If the observed surplus level is greater than zero but less than injection line$b_{1} > 0$ , the shareholders should immediately inject a certain amount of capital to bring the surplus level back to the injection line$b_{1}$ . If the observed surplus level is larger than dividend line$b_{2}$ ( $b_{2} > b_{1}$ ), any excess of the surplus over$b_{2}$ is immediately paid out as dividends to the shareholders of the company. Ruin is declared when the observed surplus level is negative. We derive the explicit expressions of the Gerber–Shiu function, the expected discounted capital injection, and the expected discounted dividend payments. Numerical illustrations are also given to analyze the effect of random observation times on actuarial quantities.

【 授权许可】

CC BY