In this paper, we consider a Gerber-Shiu discounted penalty function in Sparre Andersen risk process in which claim inter-arrival times have a phase-type （2） distribution, a distribution with a density satisfying a ...In this paper, we consider a Gerber-Shiu discounted penalty function in Sparre Andersen risk process in which claim inter-arrival times have a phase-type （2） distribution, a distribution with a density satisfying a second order linear differential equation. By conditioning on the time and the amount of the first claim, we derive a Laplace transform of the Gerber-Shiu discounted penalty function, and then we consider the joint density function of the surplus prior to ruin and the deficit at ruin and some ruin related problems. Finally, we give a numerical example to illustrate the application of the results.展开更多
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 f...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.展开更多
基金Supported by the Construction Fund for National Feature Specialty(TS11496)he Anhui Natural Science Fund for Institutions of Higher Education(KJ2010B431)he Natural Science Fund of Inner Mongolia University for the Nationalities(NMD1227)
文摘In this paper, we consider a Gerber-Shiu discounted penalty function in Sparre Andersen risk process in which claim inter-arrival times have a phase-type （2） distribution, a distribution with a density satisfying a second order linear differential equation. By conditioning on the time and the amount of the first claim, we derive a Laplace transform of the Gerber-Shiu discounted penalty function, and then we consider the joint density function of the surplus prior to ruin and the deficit at ruin and some ruin related problems. Finally, we give a numerical example to illustrate the application of the results.
基金Supported by the National Natural Sciences Foundations of China (70971037 and 71171078)the Doctoral Fund of Ministry of Education of China (20100161110022)+3 种基金China Postdoctoral Science Foundation funded project(2012M521514)Hunan Postdoctoral Scientific Program of China (2012RS4030)the Sciences Foundations of Hunan Institute of Science and Technology of China (2012Y26)the aid program for Science and Technology Research Team in Higher Educational Institutions of Hunan Province of China
文摘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.
