Gerber–Shiu discounted penalty function in a Sparre Andersen model with multi-layer dividend strategy

Yang, Hu; Zhang, Zhimin

doi:10.1016/j.insmatheco.2007.11.004

Cited by 32 publications

(20 citation statements)

References 15 publications

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“…Results related to perturbed compound Poisson risk models under multi-layer dividend strategies can be found in [31,42]. In addition, different classes of more general renewal risk models are investigated in [15,19,40,41], and some recent papers deal with risk models that incorporate various dependence structures (see, e.g., [21,38,46,48]).…”

Section: Introductionmentioning

confidence: 99%

The risk model with stochastic premiums and a multi-layer dividend strategy

Ragulina¹

2019

Modern Stochastics: Theory and Applications

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The paper deals with a generalization of the risk model with stochastic premiums where dividends are paid according to a multi-layer dividend strategy. First of all, we derive piecewise integro-differential equations for the Gerber-Shiu function and the expected discounted dividend payments until ruin. In addition, we concentrate on the detailed investigation of the model in the case of exponentially distributed claim and premium sizes and find explicit formulas for the ruin probability as well as for the expected discounted dividend payments. Lastly, numerical illustrations for some multi-layer dividend strategies are presented.Keywords Risk model with stochastic premiums, multi-layer dividend strategy, Gerber-Shiu function, expected discounted dividend payments, ruin probability, piecewise integro-differential equation 2010 MSC 91B30, 60G51

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Section: Introductionmentioning

confidence: 99%

The risk model with stochastic premiums and a multi-layer dividend strategy

Ragulina¹

2019

Modern Stochastics: Theory and Applications

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“…Piecewise integro-differential equations in matrix form would be derived and corresponding solutions would be obtained recursively in terms of analytical matrix expressions. The risk model with multi-layer (multi-threshold) dividend strategy was also studied in Albrecher and Hartinger (2007), Zhou (2007), and Yang and Zhang (2008), while the risk model discussed in Lin and Pavlova (2006) can be considered as a two-layer model. See also Badescu et al (2007) for an analysis of a threshold dividend strategy for a risk model with the Markovian arrival process, which includes the Markovian regime-switching risk model investigated in this paper as a special case.…”

Section: Introductionmentioning

confidence: 99%

The Markovian regime-switching risk model with a threshold dividend strategy

2009

Insurance: Mathematics and Economics

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“…We refer the readers to, e.g. [6], [12], [13], [14] for details. The distribution of the discounted sum of dividend payments until ruin which is an important quantity in assessing the quality of dividend strategies has been studied by [7], [11], and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Dividend moments for two classes of risk processes with phase-type interclaim times

Jiang¹

2015

HJMS

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In this paper, we consider the distribution of discounted dividend payments until ruin under a risk model with two independent classes of claims in which both of the two interclaim times have phasetype distributions and a constant dividend barrier. We obtain the integro-differential equations with boundary conditions for the momentgenerating function of the sum of the discounted dividend payments until ruin. Explicit expressions for arbitrary moments of the discounted dividend payments are derived if the distribution of the two classes claim amount both belong to the rational family. Finally, numerical illustrations are presented to show how the results are applied.

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Gerber–Shiu discounted penalty function in a Sparre Andersen model with multi-layer dividend strategy

Cited by 32 publications

References 15 publications

The risk model with stochastic premiums and a multi-layer dividend strategy

The risk model with stochastic premiums and a multi-layer dividend strategy

The Markovian regime-switching risk model with a threshold dividend strategy

Dividend moments for two classes of risk processes with phase-type interclaim times

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