Some Results for Classical Risk Process with Stochastic Return on Investments

In this paper, we discuss the classical risk process with stochastic return on investment. We prove some properties of the ruin probability, the supremum distribution before ruin and the surplus distribution at the time of ruin and derive the integro-differential equations satisfied by these distributions respectively.     

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.     

带扩散扰动项的广义双Poisson风险模型下的破产概率

本文首先在[1]-[4]讨论的基础上,将经典的破产模型推广到带扩散扰动项的广义双Po isson风险模型,即将保费收取过程和索赔总额过程同时推广到广义复合Po isson过程,以此解决在同一时刻有两张以上保单到达和两个以上顾客索赔的实际问题;接着运用鞅方法证明了破产概率满足的Lundberg不等式和一般公式在我们所建的模型下同样成立.     

相关带干扰风险模型的破产概率

本文引进了含相关类带干扰经典风险过程, 研究类之间的相关性对破产概率的影响, 主要研究类之间的相关性对其Lundberg指数的大小关系的影响.     

带有随机干扰和确定投资回报风险过程下的一些分布

我们考虑既带有随机干扰又带有确定投资回报的风险过程, 得到了破产前瞬间盈余的分布$F_{\delta}(u,x)$及破产前瞬间盈余和破产时赤字的联合分布$H_{\delta}(u,x,y)$所满足的积分表达, 连续性及二次连续可微性和积分--微分方程. 同时, 只有随机干扰的风险模型下的破产前瞬间盈余的分布及破产前瞬间盈余和破产时赤字的联合分布所满足的性质也被得到. 已有文献中的诸多有关结果均可以通过令我们结论中的某些参数特殊化为零而得到.     

带干扰的复合广义齐次Poisson过程的多险种破产概率

将复合广义齐次poisson过程的多险种风险模型推广到带干扰的一种新模型,运用鞅方法破产概率满足的Lundberg不等式和一般公式.     

随机收益环境下的破产时刻罚金折现期望

This paper considers the expected discounted penalty function Φ(u) for the perturbed compound Poisson risk model with stochastic return on investments. After presenting an integro-differential equation that the expected discounted penalty function satisfies, the paper derives the closed form solution by constructing an identical equation. The exact expression for Φ (0) is given using the Laplace transform technique when interest rate is constant. Applications of the results are given to the ruin probability and moments of the deficit at ruin.     

带干扰的多险种Cox风险模型的破产概率

考虑到保险公司在实际经营中收益所具有的不确定性和风险经营的多元化,建立了一个更现实的风险模型即带干扰的多险种Cox风险模型.运用鞅论得到了该模型最终破产概率的上界,并对Lundberg不等式作了推广.     

一类常利率下的复合Poisson-Geometric过程风险模型

将文献[6]中常利率情况下的风险模型,推广为索赔来到过程为Poisson-Geometric过程的风险模型.给出了该模型初始资产为u时生存概率所满足的积分方程,并更正了文献[6]中的错误。     

Ruin probabilities for a risk process with stochastic return on investments

In this paper, we consider a risk process with stochastic return on investments. The basic risk process is the classical risk process while the return on the investment generating process is a compound Poisson process plus a Brownian motion with positive drift. We obtain an integral equation for the ultimate ruin probability which is twice continuously differentiable under certain conditions. We then derive explicit expressions for the lower bound for the ruin probability. We also study a joint distribution related to exponential functionals of Brownian motion which is required in the derivations of the explicit expressions for the lower bound.     

随机利率下的双险种风险模型

在随机利率风险模型中,将单险种推广为双险种,推导出风险调节系数和破产概率的一般表达式.     

索赔到达过程为马氏跳过程的一类风险模型

论将索赔到达点过程由Poisson点过程推广为由马氏链的跳跃点形成的点过程，保费收取由净收入随机确定，我们得到破产概率ψ（u)及条件破产概率φi(u)满足的积分方程．     

A Markov Risk Model with Two Classes of Insurance Business

A Markov risk model with two classes of insurance business is studied. In this model, the two classes of insurance business are independent. Each of the two independent claim number processes is the number of jumps of a Markov jump process from time 0 to t, whichever has not independent increments in general. An integral equation satisfied by the ruin probability is obtained and the bounds for the convergence rate of the ruin probability are given by using a generalized renewal technique.     

一类带干扰且Cox相关的双险种风险模型

在带有随机扰动的环境中,考虑保单到达及索赔到达均为Cox点过程且两类索赔到达过程相关的一类双险种风险模型.利用鞅技巧,将破产概率的指数上界推广到了更一般的情形.     

马氏风险过程

研究了一般马氏风险过程,它是经典风险过程的拓广．具有大额索赔的风险过程用此马氏风险模型来描述是适合的．在此模型中,索赔到达过程由一点过程来描述,该点过程是一马氏跳过程从0到t时间段内的跳跃次数．主要研究了此风险模型的破产概率,得到了破产概率满足的积分方程,并应用本文引入的广更新方法,得到了破产概率的收敛速度上界．     

Ruin Theory for the Risk Process Described by PDMPs

In this paper we consider the risk process that is described by a piecewise deterministic Markov processes(PDMP).We first present the construction of the risk process and them discuss some ruin problems for this new kind of risk model.     

索赔次数为复合Poisson-Geometric过程的双险种风险模型

对索赔次数为复合Poisson-Geometric过程的双险种风险模型进行研究,给出了生存概率所满足的积分方程、指数分布下的具体表达式及有限时间内的积分—微分方程,并利用鞅方法得到了最终破产概率的Lundberg不等式和一般公式.     

常利率下带干扰负风险和模型的破产概率

本文考虑了常利率下带干扰负风险和模型的破产模型,给出了积分和积分-微分方程,并当理赔量为指数分布时给出了破产概率的具体表达式.     

双更新风险模型

本文讨论了具有两个到达过程的更新模型,在只要求点间间距的分布是绝对连续的简单条件下,利用鞅的乘积性质,得到了最终破产概率和有限时间破产概率的一个上界.