Let Ls be the last exit time from a compact set B of an elliptic diffusion process X. A moderate estimate for the distribution of Ls is obtained, and the sufficient and necessary condition for E^x（L^κB） 〈∞ is pr...Let Ls be the last exit time from a compact set B of an elliptic diffusion process X. A moderate estimate for the distribution of Ls is obtained, and the sufficient and necessary condition for E^x（L^κB） 〈∞ is proved.展开更多
Consider a discrete-time insurance risk model. Within period i, i≥ 1, Xi and Yi denote the net insurance loss and the stochastic discount factor of an insurer, respectively. Assume that {（Xi, Yi）, i≥1） form a seq...Consider a discrete-time insurance risk model. Within period i, i≥ 1, Xi and Yi denote the net insurance loss and the stochastic discount factor of an insurer, respectively. Assume that {（Xi, Yi）, i≥1） form a sequence of independent and identically distributed random vectors following a common bivariate Sarmanov distribution. In the presence of heavy-tailed net insurance losses, an asymptotic formula is derived for the finite-time ruin probability.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
The classical risk process that is perturbed by diffusion is studied. The explicit expressions for the ruin probability and the surplus distribution of the risk process at the time of ruin are obtained when the claim ...The classical risk process that is perturbed by diffusion is studied. The explicit expressions for the ruin probability and the surplus distribution of the risk process at the time of ruin are obtained when the claim amount distribution is a finite mixture of exponential distributions or a Gamma (2, α) distribution.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
The compound negative binomial model, introduced in this paper, is a discrete time version. We discuss the Markov properties of the surplus process, and study the ruin probability and the joint distributions of actuar...The compound negative binomial model, introduced in this paper, is a discrete time version. We discuss the Markov properties of the surplus process, and study the ruin probability and the joint distributions of actuarial random vectors in this model. By the strong Markov property and the mass function of a defective renewal sequence, we obtain the explicit expressions of the ruin probability, the finite-horizon ruin probability, the joint distributions of T, U（T - 1）, ｜U（T）｜ and inf U（n） （i.e., the time of ruin, the surplus immediately before ruin, the deficit at ruin and maximal deficit from ruin to recovery） and the distributions of some actuarial random vectors.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
基金Research supported in part by Tianyuan Fund ofr Mathematics of NSFC (10526021)A Grant from Ministry of Education
文摘Let Ls be the last exit time from a compact set B of an elliptic diffusion process X. A moderate estimate for the distribution of Ls is obtained, and the sufficient and necessary condition for E^x（L^κB） 〈∞ is proved.
基金Supported by the National Natural Science Foundation of China(11001052,11171065,11326175)China Postdoctoral Science Foundation(2012M520964)+2 种基金Natural Science Foundation of Jiangsu Province ofChina(BK20131339)Postdoctoral Research Program of Jiangsu Province(1302015C)Qing Lan Project and Project of Construction for Superior Subjects of Statistics&Audit Science and Technology of Jiangsu Higher Education Institutions
文摘Consider a discrete-time insurance risk model. Within period i, i≥ 1, Xi and Yi denote the net insurance loss and the stochastic discount factor of an insurer, respectively. Assume that {（Xi, Yi）, i≥1） form a sequence of independent and identically distributed random vectors following a common bivariate Sarmanov distribution. In the presence of heavy-tailed net insurance losses, an asymptotic formula is derived for the finite-time ruin probability.
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.
文摘The classical risk process that is perturbed by diffusion is studied. The explicit expressions for the ruin probability and the surplus distribution of the risk process at the time of ruin are obtained when the claim amount distribution is a finite mixture of exponential distributions or a Gamma (2, α) distribution.
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 the National Natural Science Foundation of China (No.10671197)
文摘The compound negative binomial model, introduced in this paper, is a discrete time version. We discuss the Markov properties of the surplus process, and study the ruin probability and the joint distributions of actuarial random vectors in this model. By the strong Markov property and the mass function of a defective renewal sequence, we obtain the explicit expressions of the ruin probability, the finite-horizon ruin probability, the joint distributions of T, U（T - 1）, ｜U（T）｜ and inf U（n） （i.e., the time of ruin, the surplus immediately before ruin, the deficit at ruin and maximal deficit from ruin to recovery） and the distributions of some actuarial random vectors.
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.
