The Discounted Penalty Function with Multi-Layer Dividend Strategy in the Phase-Type Risk Model

Jiang, Wuyuan; Yang, Zhaojun; Xin-ping, LI

doi:10.2139/ssrn.1983644

Cited by 4 publications

(4 citation statements)

References 18 publications

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“…A generalized Erlang(n) risk process with perturbation is investigated in [102]. As for the claim size, one finds models with arbitrary interclaim time distribution and a Coxian claim-size distribution [96], and phase-type interclaim times and claim-size distributions in the rational family [150] with an additional multi-layer dividend strategy [79]. Additional features have been introduced into the risk model, such as dependent interclaim times and claim amounts with perturbation [199], stochastic premium income [201], stochastic interest force modeled by drifted Brownian model in combination with Poisson-Geometric process [72], and two classes of claims modelled by compound Poisson and Erlang(2) renewal risk processes with a two-step premium rate under a threshold dividend strategy [121].…”

Section: Advanced Modelsmentioning

confidence: 99%

The Gerber-Shiu discounted penalty function: A review from practical perspectives

He¹,

Kawai²,

Shimizu³

et al. 2022

Preprint

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The Gerber-Shiu function provides a unified framework for the evaluation of a variety of risk quantities. Ever since its establishment, it has attracted constantly increasing interests in actuarial science, whereas the conventional research has been focused on finding analytical or semi-analytical solutions, either of which is rarely available, except for limited classes of penalty functions on rather simple risk models. In contrast to its great generality, the Gerber-Shiu function does not seem sufficiently prevalent in practice, largely due to a variety of difficulties in numerical approximation and statistical inference. To enhance research activities on such implementation aspects, we provide a full review of existing formulations and underlying surplus processes, as well as an extensive survey of analytical, semi-analytical and asymptotic methods for the Gerber-Shiu function, which altogether shed fresh light on its numerical methods and statistical inference for further developments. On the basis of an exhaustive collection of 207 references, the present survey can serve as an insightful guidebook to model and method selection from practical perspectives as well.

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Section: Advanced Modelsmentioning

confidence: 99%

The Gerber-Shiu discounted penalty function: A review from practical perspectives

He¹,

Kawai²,

Shimizu³

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…The multi-layer dividend strategy, as an extension of the threshold dividend strategy, has been investigated in several papers. For example, Zhou (2006), Lin and Sendova (2008) and Albrecher and Hartinger (2007) considered a multi-layer setting within the framework of the classical risk model, Yang and Zhang (2008) for a generalized Erlang renewal risk model and more recently, Jiang et al (2012) for a phase-type renewal model. Moreover, Badescu et al (2007b) consider a general framework for the multi-layer model via a Markovian arrival process for which they derive the Laplace-Stieltjes transform of the distribution of the time to ruin as well as the discounted joint density of the surplus prior and deficit at ruin.…”

Section: Introductionmentioning

confidence: 99%

Recursive Approaches for Multi-Layer Dividend Strategies in a Phase-Type Renewal Risk Model

Papaioannou

Ramsden²

2022

Risks

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In this paper we consider a risk model with two independent classes of insurance risks in the presence of a multi-layer dividend strategy. We assume that both of the claim number processes are renewal processes with phase-type inter-arrival times. By analysing the Markov chains associated with the two given phase-type distributions of the inter-arrival times, algorithmic schemes for the determination of explicit expressions for the Gerber–Shiu expected discounted penalty function, as well as the expected discounted dividend payments are derived, using two different approaches.

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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

Self Cite

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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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The Discounted Penalty Function with Multi-Layer Dividend Strategy in the Phase-Type Risk Model

Cited by 4 publications

References 18 publications

The Gerber-Shiu discounted penalty function: A review from practical perspectives

The Gerber-Shiu discounted penalty function: A review from practical perspectives

Recursive Approaches for Multi-Layer Dividend Strategies in a Phase-Type Renewal Risk Model

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

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