On the improved thinning risk model under a periodic dividend barrier strategy

Fuyun Sun; Yuelei Li; Fuyun Sun; Yuelei Li

doi:10.3934/math.2021779

AIMS Mathematics

2021, Volume 6, Issue 12: 13448-13463. doi: 10.3934/math.2021779

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Research article

On the improved thinning risk model under a periodic dividend barrier strategy

Fuyun Sun ¹,
Yuelei Li ^{2
,
,}

1.
School of Mathematics, Tianjin University, Tianjin 300350, China
2.
College of Management and Economics, Tianjin University, Tianjin 300072, China

Received: 14 April 2021 Accepted: 14 September 2021 Published: 18 September 2021
MSC : 91B30, 97M30

In this study, we consider a periodic dividend barrier strategy in an improved thinning risk model, which indicates that insurance companies randomly receive premiums and pay dividends. In the improved model, the premium is stochastic, and the claim counting process is a p-thinning process of the premium counting process. The integral equations satisfied by the Gerber-Shiu function and the expected discounted cumulative dividend function are derived. Explicit expressions of those actuarial functions are obtained when the claim and premium sizes are exponentially distributed. We analyze and illustrate the impact of various parameters on them and obtain the optimal barrier. Finally, a conclusion is drawn.
- thinning model,
- periodic dividend strategy,
- Gerber-Shiu function,
- stochastic premium,
- expected discounted cumulative dividend function
Citation: Fuyun Sun, Yuelei Li. On the improved thinning risk model under a periodic dividend barrier strategy[J]. AIMS Mathematics, 2021, 6(12): 13448-13463. doi: 10.3934/math.2021779

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Abstract

In this study, we consider a periodic dividend barrier strategy in an improved thinning risk model, which indicates that insurance companies randomly receive premiums and pay dividends. In the improved model, the premium is stochastic, and the claim counting process is a p-thinning process of the premium counting process. The integral equations satisfied by the Gerber-Shiu function and the expected discounted cumulative dividend function are derived. Explicit expressions of those actuarial functions are obtained when the claim and premium sizes are exponentially distributed. We analyze and illustrate the impact of various parameters on them and obtain the optimal barrier. Finally, a conclusion is drawn.

References

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