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The Phase-type Risk Model Perturbed by Diffusion under a threshold dividend strategy

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Acta Mathematicae Applicatae Sinica 2013年第1期29卷 215-224页

作者： Wu-yuan Jiang Zhou-jun Yang Department of Mathematics Hunan Institute of Science and Technology School of Finance and Statistics Hunan University

This paper considers a perturbed renewal risk process in which the inter-claim times have a phasetype distribution under a threshold dividend strategy. Integro-differential equations with certain boundary conditions for the moment-generating function and the ruth moment of the present value of all dividends until ruin are derived. Explicit expressions for the expectation of the present value of all dividends until ruin are obtained when the claim amount distribution is from the rational family. Finally, we present an example.

关键词： diffusion dividend payments threshold dividend strategy integro-differential equation rationalfamily Phase-type distribution

A Note on the Perturbed Compound Poisson Risk Model with a threshold dividend strategy

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Acta Mathematicae Applicatae Sinica 2009年第2期25卷 205-216页

作者： Bo Li Rong Wu School of Mathematical Sciences and LPMC Nankai University Tianjin 300071 China

In this paper, we consider the Perturbed Compound Poisson Risk Model with a threshold dividend strategy （PCT）. Integro-differential equations （IDE） for its Cerber-Shiu functions and dividend payments function are ... 详细信息

关键词： Gerber-Shiu function threshold dividend strategy expected discounted payments function integro-differential equation

CLASSICAL RISK MODEL WITH threshold dividend strategy

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Acta Mathematica Scientia 2008年第2期28卷 355-362页

作者：周明郭军义 CIAS Central University of Finance and Economics School of Mathematical Sciences and LPMC Nankai University

In this article, a threshold dividend strategy is used for classical risk model. Under this dividend strategy, certain probability of ruin, which occurs in case of constant barrier strategy, is avoided. Using the strong Markov property of the surplus process and the distribution of the deficit in classical risk model, the survival probability for this model is derived, which is more direct than that in Asmussen（2000, P195, Proposition 1.10）. The occupation time of non-dividend of this model is also discussed by means of Martingale method.

关键词： threshold dividend strategy ruin occupation time piecewise deterministic Markov process

The Markov-Dependent Risk Model with a threshold dividend strategy

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Wuhan University Journal of Natural Sciences 2011年第3期16卷 193-198页

作者： LIU Juan XU Jiancheng HU Hongchang School of Mathematics and Statistics Hubei Normal University Huangshi 435002 Hubei China

This paper studies a Markov-dependent risk model in which the claim occurrence and the claim amount are regulated by an external discrete time Markov process. Integro-differential equations in matrix form for the Gerber-Shiu discounted penalty function are presented. Then the analytical solutions to the equations are derived. Finally, in the two-state model, some numerical results are obtained when claim amount is exponentially distributed.

关键词： Markov-dependent threshold dividend strategy Gerber-Shiu function analytical solution

dividend Payments with a threshold strategy in a Markov-Dependent Risk Model

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Wuhan University Journal of Natural Sciences 2011年第1期16卷 11-15页

作者： LIU Juan XU Jiancheng HU Hongchang School of Mathematics and Statistics Hubei Normal UniversityHuangshi 435002 Hubei China

In this paper,a Markov-dependent risk model with a threshold strategy is considered. The expected discounted dividend payments satisfy some integro-differential equations. The analytical solutions to these systems are... 详细信息

关键词： Markov-dependent threshold dividend strategy dividend payments integro-differential equation

Optimal dividend Strategies in a Double Compound Poisson Risk Process

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Wuhan University Journal of Natural Sciences 2011年第2期16卷 133-138页

作者： LI Shijun MING Ruixing HUANG Longshengt School of Mathematics and Information Sciences JiangxiNormal University Nanchang 330022 Jiangxi China School of Management University of Science andTechnology of China Hefei 230026 Anhui China School of Sciences Zhejiang Agriculture and ForestUniversity Lin'an 311300 Zhejiang China

In this paper, we consider a double compound Poisson risk model involving two independent classes ofinsurance risks with a threshold dividend strategy. We derived the integro-differential equations （IDE） with certain boundary conditions for the present value of dividends until ruin. When the claims from both classes are exponentially distributed, we show that the threshold dividend strategy is an optimal dividend strategy.

关键词： double compound Poisson process the value function integro-differential equation threshold dividend strategy generalized Lundberg’s fundamental equation