Distribution of Deficit at Ruin for a PDMP Insurance Risk Model

In this paper we consider the risk process described by a piecewise deterministic Markov processes(PDMP). We mainly discuss the distribution of the deficit at ruin for the risk process. We derive the integrodifferential equation satisfied by this distribution. We obtain the explicit expressions for it for certain choices of the claim amount distribution.     

Ruin probabilities for a risk model with two classes of claims

In this paper we consider a risk model with two kinds of claims, whose claims number processes are Poisson process and ordinary renewal process respectively. For this model, the surplus process is not Markovian, however, it can be Markovianized by introducing a supplementary process, We prove the Markov property of the related vector processes. Because such obtained processes belong to the class of the so-called piecewise-deterministic Markov process, the extended infinitesimal generator is derived, exponential martingale for the risk process is studied. The exponential bound of ruin probability in iafinite time horizon is obtained.     

具有Vasicek利率的风险过程的破产概率的分解(英文)

In this paper, it is assumed that an insurer with a jump-diffusion risk process would invest its surplus in a bond market, and the interest structure of the bond market is assumed to follow the Vasicek interest model. This paper focuses on the studying of the ruin problems in the above compounded process. In this compounded risk model, ruin may be caused by a claim or oscillation. We decompose the ruin probability for the compounded risk process into two probabilities： the probability that ruin caused by a claim and the probability that ruin caused by oscillation. Integro-differential equations for these ruin probabilities are derived. When the claim sizes are exponentially distributed, the above-mentioned integro-differential equations can be reduced into a three-order partial differential equation.     

Ruin Probabilities of a Surplus Process Described by PDMPs

In this paper we mainly study the ruin probability of a surplus process described by a piecewise deterministic Markov process （PDMP）. An integro-differential equation for the ruin probability is derived. Under a certain assumption, it can be transformed into the ruin probability of a risk process whose premiums depend on the current reserves. Using the same argument as that in Asmussen and Nielsen, the ruin probability and its upper bounds are obtained. Finally, we give an analytic expression for ruin probability and its upper bounds when the claim-size is exponentially distributed.     

一类带干扰风险过程的破产概率的估计

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.     

THE JOINT DISTRIBUTIONS OF SOME ACTUARIAL DIAGNOSTICS FOR THE JUMP-DIFFUSION RISK PROCESS

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 L′evy process, such as the homogeneous strong Markov property and the spatial homogeneity property etc, moveover, the many properties for Brownian motion.     

EXPLICIT EXPRESSIONS FOR SOME DISTRIBUTIONS RELATED TO RUIN PROBLEMS

The classical risk process that is perturbed by diffusion is studied .The explicit expressions for the runi probability and the surplus distribution of the risk process at the time of runi are obtained when the claim amount distribution is a finite mixture of exponential distributions of a Gamma (2,α） distribution.     

Survival probability and ruin probability of a risk model

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.     

Exponential martingale for compound Poisson process with latent variable and its applications

In this article, we construct an exponential martingale for the compound Poisson process with latent variableWith the help of this exponential martingale, we provide an asymptotic behavior of the coherent entropic risk measure for the compound Poisson process and a deviation inequality for the ruin probability of the partly shifted risk process.     

Ruin probability for correlated negative risk sums model with Erlang processes

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.     

一类Cox风险过程中的三联分布(英文)

本文研究了一类Cox风险过程破产时、破产瞬间前的余额、破产时的赤字这三个重要精算量的联合分布,并给出了一些密度测度的分布.     

稀疏过程的三特征的联合分布函数

本文考虑一类人寿保险,保费到达为Po isson过程,索赔到达为p-稀疏过程,我们推导三特征的联合分布函数;破产时间,破产概率,破产前的盈余,破产赤字,并由这联合分布得破产概率的显示表达式.     

一类逐段决定风险模型罚金函数的期望(英)

本文主要考虑了一类逐段决定的风险模型的罚金函数.利用建立的积分-微分方程,我们得出了此类风险模型罚金函数期望的一般解.     

稀疏过程在破产问题中的应用

本讨论一类人寿保险的风险过程，其中保单到达服从齐次Poisson过程。而描述退保及索赔发生的计数过程分别为这一过程的q-稀疏与p-稀疏．对此模型给出其破产概率的具体上界，并与其它一类风险模型进行比较．     

一类逐段决定风险模型罚金函数的期望

本文主要考虑了一类逐段决定的风险模型的罚金函数．利用建立的积分一微分方程,我们得出了此类风险模型罚金函数期望的一般解．     

常利率下复合泊松-更新风险模型的破产问题

本文研究了常数利率下,保费收入为复合Poisson过程,理赔到达过程为一般更新过程的风险模型.利用离散化的方法,获得了该风险模型的破产概率、破产时余额分布及破产前瞬间余额分布的级数展开式,推广了文[1]和文[2]中的相关结果.     

常利率下复合泊松-更新风险模型的破产问题

本文研究了常数利率下, 保费收入为复合Poisson 过程, 理赔到达过程为一般更新过程的风险模型. 利用离散化的方法, 获得了该风险模型的破产概率、破产时余额分布及破产前瞬间余额分布的级数展开式, 推广了文[1] 和文[2] 中的相关结果.     

带随机投资收益的多险种风险过程的破产概率

由于经典模型的局限性,本文讨论了带随机投资收益的多险种风险过程,给出了破产概率的简单表达式.     

古典风险模型下的绝对破产

在古典绝对破产模型下盈余过程为是逐段决定马尔可夫过程.根据逐段决定马尔可夫过程具有马氏性和强马氏性,本文推导出了在古典风险模型下绝对破产概率的一个明确表达式.