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 stro...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.展开更多
This paper analyzes a continuous time risk model with a linear model used to model the claim process. The time is discretized stochastically using the times when claims occur, using Doob’s stopping time theorem and...This paper analyzes a continuous time risk model with a linear model used to model the claim process. The time is discretized stochastically using the times when claims occur, using Doob’s stopping time theorem and martingale inequalities to obtain expressions for the ruin probability as well as both expo- nential and non-exponential upper bounds for the ruin probability for an infinite time horizon. Numerical re- sults are included to illustrate the accuracy of the non-exponential bound.展开更多
We establish an asymptotic relation for the large-deviation probabilities of the maxima of sums of subexponential random variables centered by multiples of order statistics of i.i.d.standard uniform random variables.T...We establish an asymptotic relation for the large-deviation probabilities of the maxima of sums of subexponential random variables centered by multiples of order statistics of i.i.d.standard uniform random variables.This extends a corresponding result of Korshunov.As an application,we generalize a result of Tang,the uniform asymptotic estimate for the finite-time ruin probability,to the whole strongly subexponential class.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
In this paper, the ruin distributions were analyzed, including the distribution of surplus immediately before ruin, the distribution of claim at the time of ruin, the distribution of deficit, and the distribution of s...In this paper, the ruin distributions were analyzed, including the distribution of surplus immediately before ruin, the distribution of claim at the time of ruin, the distribution of deficit, and the distribution of surplus at the beginning of the claim period before ruin. Several integral equations for the ruin distributions were derived and some solutions under special conditions were obtained.展开更多
Consider a continuous-time renewal risk model, in which every main claim induces a delayed by-claim. Assume that the main claim sizes and the inter-arrival times form a sequence of identically distributed random pairs...Consider a continuous-time renewal risk model, in which every main claim induces a delayed by-claim. Assume that the main claim sizes and the inter-arrival times form a sequence of identically distributed random pairs, with each pair obeying a dependence structure, and so do the by-claim sizes and the delay times. Supposing that the main claim sizes with by-claim sizes form a sequence of dependent random variables with dominatedly varying tails, asymptotic estimates for the ruin probability of the surplus process are investigated, by establishing a weakly asymptotic formula, as the initial surplus tends to infinity.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 paper, we consider a hyper-exponential jump-diffusion model with a constant dividend barrier. Explicit solutions for the Laplace transform of the ruin time, and the Gerber- Shiu function are obtained via marti...In this paper, we consider a hyper-exponential jump-diffusion model with a constant dividend barrier. Explicit solutions for the Laplace transform of the ruin time, and the Gerber- Shiu function are obtained via martingale stopping.展开更多
Periodic dividend problem is a meaningful issue. Based on a compound binomial model with periodic dividend, we use a homogeneous, ergodic and irreducible discrete-time Markov chain to express the evolution from one pe...Periodic dividend problem is a meaningful issue. Based on a compound binomial model with periodic dividend, we use a homogeneous, ergodic and irreducible discrete-time Markov chain to express the evolution from one period to the subsequent of the economic or the environmental and climatic conditions. We derive some properties about the model. A system of integral equations for the expectation and the r-th moment of discounted dividends until ruin time are obtained respectively. Moreover, by using of Contraction Mapping Principle, we solve the equation system and obtain the explicit expression.展开更多
基金the National Natural Science Foundation of China(10571092)the major program of Key Research Institute of HumanitiesSocial Sciences at Universities(04JJD790006).
文摘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.
基金Supported by the National Natural Science Foundation of China (Nos. 19831020 and 70003002) and the Fundamental Research Foundation of School of Economics and Management,Tsinghua University
文摘This paper analyzes a continuous time risk model with a linear model used to model the claim process. The time is discretized stochastically using the times when claims occur, using Doob’s stopping time theorem and martingale inequalities to obtain expressions for the ruin probability as well as both expo- nential and non-exponential upper bounds for the ruin probability for an infinite time horizon. Numerical re- sults are included to illustrate the accuracy of the non-exponential bound.
基金supported by the National Natural Science Foundation of China (Grant No. 70471071)
文摘We establish an asymptotic relation for the large-deviation probabilities of the maxima of sums of subexponential random variables centered by multiples of order statistics of i.i.d.standard uniform random variables.This extends a corresponding result of Korshunov.As an application,we generalize a result of Tang,the uniform asymptotic estimate for the finite-time ruin probability,to the whole strongly subexponential class.
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.
文摘In this paper, the ruin distributions were analyzed, including the distribution of surplus immediately before ruin, the distribution of claim at the time of ruin, the distribution of deficit, and the distribution of surplus at the beginning of the claim period before ruin. Several integral equations for the ruin distributions were derived and some solutions under special conditions were obtained.
基金Supported by the National Natural Science Foundation of China(11301481,11201422,11371321)Zhejiang Provincial Key Research Base for Humanities and Social Science Research(Statistics)Foundation for Young Talents of ZJGSU(1020XJ1314019)
文摘Consider a continuous-time renewal risk model, in which every main claim induces a delayed by-claim. Assume that the main claim sizes and the inter-arrival times form a sequence of identically distributed random pairs, with each pair obeying a dependence structure, and so do the by-claim sizes and the delay times. Supposing that the main claim sizes with by-claim sizes form a sequence of dependent random variables with dominatedly varying tails, asymptotic estimates for the ruin probability of the surplus process are investigated, by establishing a weakly asymptotic formula, as the initial surplus tends to infinity.
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 Natural Science Foundation of Jiangsu Province(BK20130260)the National Natural Science Foundation of China(11301369)the Postdoctoral Science Foundation of China(2013M540371)
文摘In this paper, we consider a hyper-exponential jump-diffusion model with a constant dividend barrier. Explicit solutions for the Laplace transform of the ruin time, and the Gerber- Shiu function are obtained via martingale stopping.
基金Supported by NSFC(Grant Nos.11171101,11271121)Doctoral Fund of Education Ministry of China(Grant No.20104306110001)+1 种基金Graduate Student Research Innovation Project in Hu’nan Province(Grant No.CX2013B215)the Construct Program of the Key Discipline in Hu’nan Province,Science and Technology Program of Hu’nan Province(Grant No.2014FJ3058)
文摘Periodic dividend problem is a meaningful issue. Based on a compound binomial model with periodic dividend, we use a homogeneous, ergodic and irreducible discrete-time Markov chain to express the evolution from one period to the subsequent of the economic or the environmental and climatic conditions. We derive some properties about the model. A system of integral equations for the expectation and the r-th moment of discounted dividends until ruin time are obtained respectively. Moreover, by using of Contraction Mapping Principle, we solve the equation system and obtain the explicit expression.
