In this paper, we investigate the Gerber-Shiu discounted penalty function for the surplus process described by a piecewise deterministic Markov process （PDMP）. We derive an integral equation for the Gerber-Shiu disc...In this paper, we investigate the Gerber-Shiu discounted penalty function for the surplus process described by a piecewise deterministic Markov process （PDMP）. We derive an integral equation for the Gerber-Shiu discounted penalty function, and obtain the exact solution when the initial surplus is zero. Dickson formulae are also generalized to the present surplus process.展开更多
The purpose of this paper is to consider the expected value of a discounted penalty due at ruin in the Erlang（2） risk process under constant interest force. An integro-differential equation satisfied by the expected...The purpose of this paper is to consider the expected value of a discounted penalty due at ruin in the Erlang（2） risk process under constant interest force. An integro-differential equation satisfied by the expected value and a second-order differential equation for the Laplace transform of the expected value are derived. In addition, the paper will present the recursive algorithm for the joint distribution of the surplus immediately before ruin and the deficit at ruin. Finally, by the differential equation, the defective renewal equation and the explicit expression for the expected value are given in the interest-free case.展开更多
We consider the Sparre Andersen risk process in the presence of a constant dividend barrier, and propose a new expected discounted penalty function which is different from that of Gerber and Shiu. We find that iterati...We consider the Sparre Andersen risk process in the presence of a constant dividend barrier, and propose a new expected discounted penalty function which is different from that of Gerber and Shiu. We find that iteration mothed can be used to compute the values of expected discounted dividends until ruin and the new penalty function. Applying the new function and the recursion method proposed in Section 5, we obtain the arbitrary moments of discounted dividend payments until ruin.展开更多
In this paper,we study a general Lévy risk process with positive and negative jumps.A renewal equation and an infinite series expression are obtained for the expected discounted penalty function of this risk mode...In this paper,we study a general Lévy risk process with positive and negative jumps.A renewal equation and an infinite series expression are obtained for the expected discounted penalty function of this risk model.We also examine some asymptotic behaviors for the ruin probability as the initial capital tends to infinity.展开更多
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
基金Supported by National Natural Science Foundation of China (Grant Nos. 10926161, 10901086, 10871102)National Basic Research Program of China (973 Program) 2007CB814905the Research Fund for the Doctorial Program of Higher Education
文摘In this paper, we investigate the Gerber-Shiu discounted penalty function for the surplus process described by a piecewise deterministic Markov process （PDMP）. We derive an integral equation for the Gerber-Shiu discounted penalty function, and obtain the exact solution when the initial surplus is zero. Dickson formulae are also generalized to the present surplus process.
基金supported by the National Natural science Foundation of china(70271069)
文摘The purpose of this paper is to consider the expected value of a discounted penalty due at ruin in the Erlang（2） risk process under constant interest force. An integro-differential equation satisfied by the expected value and a second-order differential equation for the Laplace transform of the expected value are derived. In addition, the paper will present the recursive algorithm for the joint distribution of the surplus immediately before ruin and the deficit at ruin. Finally, by the differential equation, the defective renewal equation and the explicit expression for the expected value are given in the interest-free case.
文摘We consider the Sparre Andersen risk process in the presence of a constant dividend barrier, and propose a new expected discounted penalty function which is different from that of Gerber and Shiu. We find that iteration mothed can be used to compute the values of expected discounted dividends until ruin and the new penalty function. Applying the new function and the recursion method proposed in Section 5, we obtain the arbitrary moments of discounted dividend payments until ruin.
基金Supported by the National Natural Science Foundation of China (No.10771119)the Research Fund forthe Doctoral Program of Higher Education of China (No.20093705110002)
文摘In this paper,we study a general Lévy risk process with positive and negative jumps.A renewal equation and an infinite series expression are obtained for the expected discounted penalty function of this risk model.We also examine some asymptotic behaviors for the ruin probability as the initial capital tends to infinity.
基金Supported by the National Natural Science Foundation of China(11401498,61561025)Science and Technology Planning Project of Jiangxi Provincial Education Department(GJJ150401)the Fundamental Research Funds for the Central Universities(20720140525)
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The Philosophy and Social Science Fund of Hunan Province(17YBA290)the Scientific Research Fund of Hunan Provincial Department of Education(17K05717C1001)~~
