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Open AccessArticle

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

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School of Insurance, Shandong University of Finance and Economics, Jinan 250014, China
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College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China
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School of Mathematic and Quantitative Economics, Shandong University of Finance and Economics, Jinan 250014, China
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School of Science, Shandong Jiaotong University, Jinan 250357, China
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School of Computer Science & Technology, Shandong University of Finance and Economics, Jinan 250014, China
*
Authors to whom correspondence should be addressed.
Mathematics 2020, 8(4), 511; https://doi.org/10.3390/math8040511
Received: 18 February 2020 / Revised: 22 March 2020 / Accepted: 25 March 2020 / Published: 2 April 2020
(This article belongs to the Special Issue Probability, Statistics and Their Applications)
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. View Full-Text
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 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
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Yu, W.; Guo, P.; Wang, Q.; Guan, G.; Yang, Q.; Huang, Y.; Yu, X.; Jin, B.; Cui, C. On a Periodic Capital Injection and Barrier Dividend Strategy in the Compound Poisson Risk Model. Mathematics 2020, 8, 511.

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