Researchers from Shandong University of Finance and Economics Report Recent Findings in Differential Equations (Randomized observation periods for compound Poisson risk model with capital injection and barrier dividend)

2021 MAY 14 (NewsRx) -- By a News Reporter-Staff News Editor at Math Daily News -- Data detailed on differential equations have been presented. According to news reporting originating from Shandong University of Finance and Economics by NewsRx correspondents, research stated, “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.”

Financial supporters for this research include the National Social Science Foundation of China; the Taishan Scholars Program of Shandong Province; the Humanities and Social Sciences Project of the Ministry Education of China; the Natural Science Foundation of Shandong Province.

Our news journalists obtained a quote from the research from Shandong University of Finance and Economics: “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 Erlang ( n ) $operatorname{Erlang}(n)$ distribution. If the observed surplus level is greater than zero but less than injection line b 1 > 0 $b_{1} > 0$ , the shareholders should immediately inject a certain amount of capital to bring the surplus level back to the injection line b 1 $b_{1}$. If the observed surplus level is larger than dividend line b 2 $b_{2}$ ( b 2 > b 1 $b_{2} > b_{1}$ ), any excess of the surplus over b 2 $b_{2}$ 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.”

According to the news reporters, the research concluded: “Numerical illustrations are also given to analyze the effect of random observation times on actuarial quantities.”

For more information on this research see: Randomized observation periods for compound Poisson risk model with capital injection and barrier dividend. Advances in Difference Equations, 2021,2021(1):1-24. (Advances in Difference Equations - http://www.advancesindifferenceequations.com/). The publisher for Advances in Difference Equations is SpringerOpen.

A free version of this journal article is available at https://doi.org/10.1186/s13662-021-03378-w.

Our news editors report that additional information may be obtained by contacting Wenguang Yu, School of Insurance, Shandong University of Finance and Economics. Additional authors for this research include Peng Guo, Qi Wang, Guofeng Guan, Yujuan Huang, Xinliang Yu.

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