Consider a nonstandard continuous-time bidimensional risk model with constant force of interest,in which the two classes of claims with subexponential distributions satisfy a general dependence structure and each pair...Consider a nonstandard continuous-time bidimensional risk model with constant force of interest,in which the two classes of claims with subexponential distributions satisfy a general dependence structure and each pair of the claim-inter-arrival times is arbitrarily dependent.Under some mild conditions,we achieve a locally uniform approximation of the finite-time ruin probability for all time horizon within a finite interval.If we further assume that each pair of the claim-inter-arrival times is negative quadrant dependent and the two classes of claims are consistently-varying-tailed,it shows that the above obtained approximation is also globally uniform for all time horizon within an infinite interval.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, 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
This article considers a risk model as in Yuen et al. (2002). Under this model the two claim number processes are correlated. Claim occurrence of both classes relate to Poisson and Erlang processes. The formulae is ...This article considers a risk model as in Yuen et al. (2002). Under this model the two claim number processes are correlated. Claim occurrence of both classes relate to Poisson and Erlang processes. The formulae is derived for the distribution of the surplus immediately before ruin, for the distribution of the surplus immediately after ruin and the joint distribution of the surplus immediately before and after ruin. The asymptotic property of these ruin functions is also investigated.展开更多
In this paper,a class of risk processes perturbed by diffusion are considered. The Lundberg inequalities for the ruin probability are obtained.The size of the Lundberg exponents for different kinds of risk model is co...In this paper,a class of risk processes perturbed by diffusion are considered. The Lundberg inequalities for the ruin probability are obtained.The size of the Lundberg exponents for different kinds of risk model is compared. The numerical illustration for the impact of the parameters on the ruin probability is given.展开更多
This article deals with the problem of minimizing ruin probability under optimal control for the continuous-time compound binomial model with investment. The jump mechanism in our article is different from that of Liu...This article deals with the problem of minimizing ruin probability under optimal control for the continuous-time compound binomial model with investment. The jump mechanism in our article is different from that of Liu et al [4]. Comparing with [4], the introduction of the investment, and hence, the additional Brownian motion term, makes the problem technically challenging. To overcome this technical difficulty, the theory of change of measure is used and an exponential martingale is obtained by virtue of the extended generator. The ruin probability is minimized through maximizing adjustment coefficient in the sense of Lundberg bounds. At the same time, the optimal investment strategy is 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
We consider a risk model with a premium rate which varies with the level of free reserves. In this model, the occurrence of claims is described by a Cox process with Markov intensity process, and the influence of stoc...We consider a risk model with a premium rate which varies with the level of free reserves. In this model, the occurrence of claims is described by a Cox process with Markov intensity process, and the influence of stochastic factors is considered by adding a diffusion process. The integro-differential equation for the ruin probability is derived by a infinitesimal method. Key words ruin probability - variable premium rate - diffusion process - Markov intensity CLC number O 211.9 Foundation item: Supported by the National Natural Science Foundation of China (10071058, 70273029)展开更多
We consider a discrete time risk model in which the net payout (insurance risk) {Xk, k = 1, 2,...} are assumed to take real values and belong to the heavy-tailed class L∩ D and the discount factors (financial risk...We consider a discrete time risk model in which the net payout (insurance risk) {Xk, k = 1, 2,...} are assumed to take real values and belong to the heavy-tailed class L∩ D and the discount factors (financial risk) {Yk, k = 1,2,...} concentrate on [θ, L], where 0 〈 0 〈 1, L 〈 ∞, {Xk, k = 1,2,...}, and {Yk, k=1,2,...} are assumed to be mutually independent. We investigate the asymptotic behavior of the ruin probability within a finite time horizon as the initial capital tends to infinity, and figure out that the convergence holds uniformly for all n ≥ 1, which is different from Tang Q H and Tsitsiashvili G (Adv Appl Prob, 2004, 36: 1278-1299).展开更多
In this paper, a new risk model is studied in which the rate of premium income is regarded as a random variable, the arrival of insurance policies is a Poisson process and the process of claim occurring is p-thinning ...In this paper, a new risk model is studied in which the rate of premium income is regarded as a random variable, the arrival of insurance policies is a Poisson process and the process of claim occurring is p-thinning process. The integral representations of the survival probability are gotten. The explicit formula of the survival probability on the infinite interval is obtained in the special casc cxponential distribution.The Lundberg inequality and the common formula of the ruin probability are gotten in terms of some techniques from martingale theory.展开更多
Let R(t)=u+ct-∑ I=1^N(t) Xi,t≥0 be the renewal risk model, with Fx(x)being the distribution function of the claim amount X. Let ψ(u) be the ruin probability with initial surplus u. Under the condition of F...Let R(t)=u+ct-∑ I=1^N(t) Xi,t≥0 be the renewal risk model, with Fx(x)being the distribution function of the claim amount X. Let ψ(u) be the ruin probability with initial surplus u. Under the condition of Fx(x) ∈ S^*(γ),y ≥ 0, by the geometric sum method, we derive the local asymptotic behavior for ψ(u,u + z] for every 0 ( z ( oo, On one hand, the asymptotic behavior of ψ(u) can be derived from the result obtained. On the other hand, the result of this paper can be applied to the insurance risk management of an insurance company.展开更多
This paper studies a Sparre Andersen negative risk sums model in which the distribution of "interclaim" time is that of a sum of n independent exponential random variables. Thus, the Erlang(n) model is a special c...This paper studies a Sparre Andersen negative risk sums model in which the distribution of "interclaim" time is that of a sum of n independent exponential random variables. Thus, the Erlang(n) model is a special case. On this basis the correlated negative risk sums process with the common Erlang process is considered. Integro-differential equations with boundary conditions for ψ(u) are given. For some special cases a closed-form expression for ψ(u) is derived.展开更多
In this article, the risk process perturbed by diffusion under interest force is considered, the continuity and twice continuous differentiability for Фδ(u,w) are discussed,the Feller expression and the integro-di...In this article, the risk process perturbed by diffusion under interest force is considered, the continuity and twice continuous differentiability for Фδ(u,w) are discussed,the Feller expression and the integro-differential equation satisfied by Фδ (u ,w) are derived. Finally, the decomposition of Фδ(u,w) is discussed, and some properties of each decomposed part of Фδ(u,w) are obtained. The results can be reduced to some ones in Gerber and Landry's,Tsai and Willmot's, and Wang's works by letting parameter δ and (or) a be zero.展开更多
The spectrally negative Lévy risk model with random observation times is considered in this paper,in which both dividends and capital injections are made at some independent Poisson observation times.Under the ab...The spectrally negative Lévy risk model with random observation times is considered in this paper,in which both dividends and capital injections are made at some independent Poisson observation times.Under the absolute ruin,the expected discounted dividends and the expected discounted capital injections are discussed.We also study the joint Laplace transforms including the absolute ruin time and the total dividends or the total capital injections.All the results are expressed in scale functions.展开更多
A model was proposed for addressing investment risk of the flee reserve in the form of credit or currency risk. This risk was expressed by a constant amount K ( e. g., securitization) upon an interest-increasing eve...A model was proposed for addressing investment risk of the flee reserve in the form of credit or currency risk. This risk was expressed by a constant amount K ( e. g., securitization) upon an interest-increasing event and a random variable Z representing the recovery rate of a bond or a devaluation factor. The model equation is an integro-differential equation with deviating arguments. The analytical solutions were obtained for the probability of survival as Z is a discrete random variable and as Z is a continuous random variable respectively.展开更多
In this article, we consider the perturbed classical surplus model. We study the probability that ruin occurs at each instant of claims, the probability that ruin occurs between two consecutive claims occurrences, as ...In this article, we consider the perturbed classical surplus model. We study the probability that ruin occurs at each instant of claims, the probability that ruin occurs between two consecutive claims occurrences, as well as the distribution of the ruin time that lies in between two consecutive claims. We give some finite expressions depending on derivatives for Laplace transforms, which can allow computation of the probabilities concerning with claim occurrences. Further, we present some insight on the shapes of probability functions involved.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
Consider an insurance risk model, in which the surplus process satisfies a recursive equationU n =U n?1(1+r n )?X n forn≥1, whereU 0=x≥0 is the initial surplus, {r n ;n≥1} the interest rate sequence, {X n ;n≥1} th...Consider an insurance risk model, in which the surplus process satisfies a recursive equationU n =U n?1(1+r n )?X n forn≥1, whereU 0=x≥0 is the initial surplus, {r n ;n≥1} the interest rate sequence, {X n ;n≥1} the sequence of i. i. d. real-valued random variables with common distribution functionF, which denotes the gross loss during thenth year. We investigate the ruin probability within a finite time horizon and give the asymptotic result asx→∞. Key words variable interest rate - extend regular variation - finite time ruin probability CLC number O 211.9 Foundation item: Supported by the National Natural Science Foundation of China (10071058, 70273029)Biography: WEI Xiao (1979-), female, Ph. D candidate, research direction: large deviations and its applications, insurance mathematics.展开更多
The insurance industry typically exploits ruin theory on collected data to gain more profits.However,state-of-art approaches fail to consider the dependency of the intensity of claim numbers,resulting in the loss of a...The insurance industry typically exploits ruin theory on collected data to gain more profits.However,state-of-art approaches fail to consider the dependency of the intensity of claim numbers,resulting in the loss of accuracy.In this work,we establish a new risk model based on traditional AR(1)time series,and propose a fine-gained insurance model which has a dependent data structure.We leverage Newton iteration method to figure out the adjustment coefficient and evaluate the exponential upper bound of the ruin probability.We claim that our model significantly improves the precision of insurance model and explores an interesting direction for future research.展开更多
基金Supported by the Natural Science Foundation of China(12071487,11671404)the Natural Science Foundation of Anhui Province(2208085MA06)+1 种基金the Provincial Natural Science Research Project of Anhui Colleges(KJ2021A0049,KJ2021A0060)Hunan Provincial Innovation Foundation for Postgraduate(CX20200146)。
文摘Consider a nonstandard continuous-time bidimensional risk model with constant force of interest,in which the two classes of claims with subexponential distributions satisfy a general dependence structure and each pair of the claim-inter-arrival times is arbitrarily dependent.Under some mild conditions,we achieve a locally uniform approximation of the finite-time ruin probability for all time horizon within a finite interval.If we further assume that each pair of the claim-inter-arrival times is negative quadrant dependent and the two classes of claims are consistently-varying-tailed,it shows that the above obtained approximation is also globally uniform for all time horizon within an infinite interval.
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.
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This work was supported in part by the National Natural Science Foundation of China (10071058, 70273029) the Ministry of Education of China.
文摘This article considers a risk model as in Yuen et al. (2002). Under this model the two claim number processes are correlated. Claim occurrence of both classes relate to Poisson and Erlang processes. The formulae is derived for the distribution of the surplus immediately before ruin, for the distribution of the surplus immediately after ruin and the joint distribution of the surplus immediately before and after ruin. The asymptotic property of these ruin functions is also investigated.
文摘In this paper,a class of risk processes perturbed by diffusion are considered. The Lundberg inequalities for the ruin probability are obtained.The size of the Lundberg exponents for different kinds of risk model is compared. The numerical illustration for the impact of the parameters on the ruin probability is given.
基金supported by the Nature Science Foundation of Hebei Province(A2014202202)supported by the Nature Science Foundation of China(11471218)
文摘This article deals with the problem of minimizing ruin probability under optimal control for the continuous-time compound binomial model with investment. The jump mechanism in our article is different from that of Liu et al [4]. Comparing with [4], the introduction of the investment, and hence, the additional Brownian motion term, makes the problem technically challenging. To overcome this technical difficulty, the theory of change of measure is used and an exponential martingale is obtained by virtue of the extended generator. The ruin probability is minimized through maximizing adjustment coefficient in the sense of Lundberg bounds. At the same time, the optimal investment strategy is 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.
文摘We consider a risk model with a premium rate which varies with the level of free reserves. In this model, the occurrence of claims is described by a Cox process with Markov intensity process, and the influence of stochastic factors is considered by adding a diffusion process. The integro-differential equation for the ruin probability is derived by a infinitesimal method. Key words ruin probability - variable premium rate - diffusion process - Markov intensity CLC number O 211.9 Foundation item: Supported by the National Natural Science Foundation of China (10071058, 70273029)
基金supported by the National Natural Science Foundation of China (10671149)the Ministry of Education of China, the Natural Science Foundation of Jiangxi(2008GQS0035)the Foundation of the Hubei Provincial Department of Education (B20091107)
文摘We consider a discrete time risk model in which the net payout (insurance risk) {Xk, k = 1, 2,...} are assumed to take real values and belong to the heavy-tailed class L∩ D and the discount factors (financial risk) {Yk, k = 1,2,...} concentrate on [θ, L], where 0 〈 0 〈 1, L 〈 ∞, {Xk, k = 1,2,...}, and {Yk, k=1,2,...} are assumed to be mutually independent. We investigate the asymptotic behavior of the ruin probability within a finite time horizon as the initial capital tends to infinity, and figure out that the convergence holds uniformly for all n ≥ 1, which is different from Tang Q H and Tsitsiashvili G (Adv Appl Prob, 2004, 36: 1278-1299).
文摘In this paper, a new risk model is studied in which the rate of premium income is regarded as a random variable, the arrival of insurance policies is a Poisson process and the process of claim occurring is p-thinning process. The integral representations of the survival probability are gotten. The explicit formula of the survival probability on the infinite interval is obtained in the special casc cxponential distribution.The Lundberg inequality and the common formula of the ruin probability are gotten in terms of some techniques from martingale theory.
基金Supported by the National Natural Science Foundation of China (70273029)
文摘Let R(t)=u+ct-∑ I=1^N(t) Xi,t≥0 be the renewal risk model, with Fx(x)being the distribution function of the claim amount X. Let ψ(u) be the ruin probability with initial surplus u. Under the condition of Fx(x) ∈ S^*(γ),y ≥ 0, by the geometric sum method, we derive the local asymptotic behavior for ψ(u,u + z] for every 0 ( z ( oo, On one hand, the asymptotic behavior of ψ(u) can be derived from the result obtained. On the other hand, the result of this paper can be applied to the insurance risk management of an insurance company.
基金Supported by the Foundation of Suzhou Science and Technology University
文摘This paper studies a Sparre Andersen negative risk sums model in which the distribution of "interclaim" time is that of a sum of n independent exponential random variables. Thus, the Erlang(n) model is a special case. On this basis the correlated negative risk sums process with the common Erlang process is considered. Integro-differential equations with boundary conditions for ψ(u) are given. For some special cases a closed-form expression for ψ(u) is derived.
文摘In this article, the risk process perturbed by diffusion under interest force is considered, the continuity and twice continuous differentiability for Фδ(u,w) are discussed,the Feller expression and the integro-differential equation satisfied by Фδ (u ,w) are derived. Finally, the decomposition of Фδ(u,w) is discussed, and some properties of each decomposed part of Фδ(u,w) are obtained. The results can be reduced to some ones in Gerber and Landry's,Tsai and Willmot's, and Wang's works by letting parameter δ and (or) a be zero.
基金Supported by the National Natural Science Foundation of China(11701319,11571198).
文摘The spectrally negative Lévy risk model with random observation times is considered in this paper,in which both dividends and capital injections are made at some independent Poisson observation times.Under the absolute ruin,the expected discounted dividends and the expected discounted capital injections are discussed.We also study the joint Laplace transforms including the absolute ruin time and the total dividends or the total capital injections.All the results are expressed in scale functions.
基金Project supported by National Natural Science Foundation of China (Grant Nos. 10471088, 60572126)
文摘A model was proposed for addressing investment risk of the flee reserve in the form of credit or currency risk. This risk was expressed by a constant amount K ( e. g., securitization) upon an interest-increasing event and a random variable Z representing the recovery rate of a bond or a devaluation factor. The model equation is an integro-differential equation with deviating arguments. The analytical solutions were obtained for the probability of survival as Z is a discrete random variable and as Z is a continuous random variable respectively.
基金supported by National Ba-sic Research Program of China (973 Program, 2007CB814905)the Natural Science Foundation of China(10871102)
文摘In this article, we consider the perturbed classical surplus model. We study the probability that ruin occurs at each instant of claims, the probability that ruin occurs between two consecutive claims occurrences, as well as the distribution of the ruin time that lies in between two consecutive claims. We give some finite expressions depending on derivatives for Laplace transforms, which can allow computation of the probabilities concerning with claim occurrences. Further, we present some insight on the shapes of probability functions involved.
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Consider an insurance risk model, in which the surplus process satisfies a recursive equationU n =U n?1(1+r n )?X n forn≥1, whereU 0=x≥0 is the initial surplus, {r n ;n≥1} the interest rate sequence, {X n ;n≥1} the sequence of i. i. d. real-valued random variables with common distribution functionF, which denotes the gross loss during thenth year. We investigate the ruin probability within a finite time horizon and give the asymptotic result asx→∞. Key words variable interest rate - extend regular variation - finite time ruin probability CLC number O 211.9 Foundation item: Supported by the National Natural Science Foundation of China (10071058, 70273029)Biography: WEI Xiao (1979-), female, Ph. D candidate, research direction: large deviations and its applications, insurance mathematics.
基金the Natural Science Foundation of Jilin Province(No.20180101216JC)the National Natural Science Foundation of China(No.11871028).
文摘The insurance industry typically exploits ruin theory on collected data to gain more profits.However,state-of-art approaches fail to consider the dependency of the intensity of claim numbers,resulting in the loss of accuracy.In this work,we establish a new risk model based on traditional AR(1)time series,and propose a fine-gained insurance model which has a dependent data structure.We leverage Newton iteration method to figure out the adjustment coefficient and evaluate the exponential upper bound of the ruin probability.We claim that our model significantly improves the precision of insurance model and explores an interesting direction for future research.