In this article, we consider an optimal proportional reinsurance with constant dividend barrier. First, we derive the Hamilton-Jacobi-Bellman equation satisfied by the expected discounted dividend payment, and then ge...In this article, we consider an optimal proportional reinsurance with constant dividend barrier. First, we derive the Hamilton-Jacobi-Bellman equation satisfied by the expected discounted dividend payment, and then get the optimal stochastic control and the optimal constant barrier. Secondly, under the optimal constant dividend barrier strategy, we consider the moments of the discounted dividend payment and their explicit expressions are given. Finally, we discuss the Laplace transform of the time of ruin and its explicit expression is also given.展开更多
A dual model of the perturbed classical compound Poisson risk model is considered under a constant dividend barrier. A new method is used in deriving the boundary condition of the equation for the expectation function...A dual model of the perturbed classical compound Poisson risk model is considered under a constant dividend barrier. A new method is used in deriving the boundary condition of the equation for the expectation function by studying the local time of a related process. We obtain the expression for the expected discount dividend function in terms of those in the corresponding perturbed compound Poisson risk model without barriers. A special case in which the gain size is phase-type distributed is illustrated. We also consider the existence of the optimal dividend level.展开更多
We consider the discrete risk model with exponential claim sizes. We derive the finite explicit elementary expression for the joint density function of three characteristics： the time of ruin, the surplus immediately...We consider the discrete risk model with exponential claim sizes. We derive the finite explicit elementary expression for the joint density function of three characteristics： the time of ruin, the surplus immediately before ruin, and the deficit at ruin. By using the explicit joint density function, we give a concise expression for the Gerber-Shiu function with no dividends. FinMly, we obtain an integral equation for the Gerber-Shiu function under the barrier dividend strategy. The solution can be expressed as a combination of the Gerber-Shiu function without dividends and the solution of the corresponding homogeneous integral equation. This latter function is given clearly by means of the Gerber- Shiu function without dividends .展开更多
With the ever-evolving of modern risk theory,more and more attention should be paid to the modification of the classical risk theory. In this paper a risk process with premiums dependent on the current reserve is cons...With the ever-evolving of modern risk theory,more and more attention should be paid to the modification of the classical risk theory. In this paper a risk process with premiums dependent on the current reserve is considered. An explicit expression for the joint distribution of the time of ruin,the surplus immediately before ruin and the deficit at ruin is derived. Finally,some important actuarial diagnostics including the ultimate ruin probability is investigated.展开更多
A modified classical model with a dividend barrier is considered. It is shown that there is a simple approximation formula for the time of ruin when the level of dividend barrier is high and the claim sizes have a dis...A modified classical model with a dividend barrier is considered. It is shown that there is a simple approximation formula for the time of ruin when the level of dividend barrier is high and the claim sizes have a distribution that belongs to S（γ） with γ 〉0.展开更多
In this article, the joint distributions of several actuarial diagnostics which are important to insurers＇ running for the jump-diffusion risk process are examined. They include the ruin time, the time of the surplus...In this article, the joint distributions of several actuarial diagnostics which are important to insurers＇ running for the jump-diffusion risk process are examined. They include the ruin time, the time of the surplus process leaving zero ultimately （simply, the ultimately leaving-time）, the surplus immediately prior to ruin, the supreme profits before ruin, the supreme profits and deficit until it leaves zero ultimately and so on. The explicit expressions for their distributions are obtained mainly by the various properties of Levy process, such as the homogeneous strong Markov property and the spatial homogeneity property etc, moveover, the many properties for Brownian motion.展开更多
基金a grant from National Natural Science Foundation of China (10671072)Doctoral Program Foundation of the Ministry of Education of China (20060269016)+1 种基金the National Basic Research Program (973 Program,2007CB814904) of Chinathe NSF of Anhui Educational Bureau (KJ2008B243)
基金Supported in part by the National Natural Science Foun-dation of China and the Ministry of Education of China
文摘In this article, we consider an optimal proportional reinsurance with constant dividend barrier. First, we derive the Hamilton-Jacobi-Bellman equation satisfied by the expected discounted dividend payment, and then get the optimal stochastic control and the optimal constant barrier. Secondly, under the optimal constant dividend barrier strategy, we consider the moments of the discounted dividend payment and their explicit expressions are given. Finally, we discuss the Laplace transform of the time of ruin and its explicit expression is also given.
基金the National Basic Research Program of China (973 Program)(No.2007CB814905)the National Natural Science Foundation of China (No.10571092)the Research Fund of the Doctorial Program of Higher Education
文摘A dual model of the perturbed classical compound Poisson risk model is considered under a constant dividend barrier. A new method is used in deriving the boundary condition of the equation for the expectation function by studying the local time of a related process. We obtain the expression for the expected discount dividend function in terms of those in the corresponding perturbed compound Poisson risk model without barriers. A special case in which the gain size is phase-type distributed is illustrated. We also consider the existence of the optimal dividend level.
基金Acknowledgements This work was supported in part by the National Natural Science Foundation of China （Crant Nos. 11226203, 11226204, 11171164, 11271385, 11401436）.
文摘We consider the discrete risk model with exponential claim sizes. We derive the finite explicit elementary expression for the joint density function of three characteristics： the time of ruin, the surplus immediately before ruin, and the deficit at ruin. By using the explicit joint density function, we give a concise expression for the Gerber-Shiu function with no dividends. FinMly, we obtain an integral equation for the Gerber-Shiu function under the barrier dividend strategy. The solution can be expressed as a combination of the Gerber-Shiu function without dividends and the solution of the corresponding homogeneous integral equation. This latter function is given clearly by means of the Gerber- Shiu function without dividends .
基金Ministry of Education in China(MOE)Youth Projects of Humanities and Social Sciences(Nos.14YJCZH048,15YJCZH204)National Natural Science Foundations of China(Nos.11401436,11601382,11101434,11571372)+2 种基金National Social Science Foundation of China(No.15BJY122)Hunan Provincial Natural Science Foundation of China(No.13JJ5043)Mathematics and Interdisciplinary Sciences Project,Central South University
文摘With the ever-evolving of modern risk theory,more and more attention should be paid to the modification of the classical risk theory. In this paper a risk process with premiums dependent on the current reserve is considered. An explicit expression for the joint distribution of the time of ruin,the surplus immediately before ruin and the deficit at ruin is derived. Finally,some important actuarial diagnostics including the ultimate ruin probability is investigated.
基金The National Natural Science Foundations of China (grant No.10271062 and No.10471076)the Natural Science Foundation of Sandong Province(Y2004A06)the Postdoctoral Research Fund of Qufu Normal University.
基金Supported by the NNSF of China(10471076)the Science Foundation of Qufu Normal University.
文摘A modified classical model with a dividend barrier is considered. It is shown that there is a simple approximation formula for the time of ruin when the level of dividend barrier is high and the claim sizes have a distribution that belongs to S（γ） with γ 〉0.
基金Supported by the National Natural Sci-ence Foundations of China (10271062 and 10471119)the Natural Science Foundation of Shandong Province(Y2004A06, Y2008A12, and ZR2009AL015)+1 种基金the Science Foundations of Shandong Provincial Education Department (J07yh05)the Science Foundations of Qufu Normal University (XJ0713, Bsqd200517)
文摘In this article, the joint distributions of several actuarial diagnostics which are important to insurers＇ running for the jump-diffusion risk process are examined. They include the ruin time, the time of the surplus process leaving zero ultimately （simply, the ultimately leaving-time）, the surplus immediately prior to ruin, the supreme profits before ruin, the supreme profits and deficit until it leaves zero ultimately and so on. The explicit expressions for their distributions are obtained mainly by the various properties of Levy process, such as the homogeneous strong Markov property and the spatial homogeneity property etc, moveover, the many properties for Brownian motion.
