保费收入率与索赔到达率均依赖于当前储备金的风险模型的破产问题

本文建立了保费收入率与索赔到达均依赖于当前盈余额的保险模型.将这一模型纳入逐段决定马尔可夫过程的框架,破产时刻就是这一逐段决定马尔可夫过程的端时.我们用鞅方法得到了保费收入率与索赔到达率均依赖于当前盈余额的风险模型的破产概率的确切表达式.     

Markov-modulated风险模型破产前最大盈余额与破产赤字的联合分布

应用逐段决定马尔可夫过程理论及补充变量技巧,使Markov-modulated风险过程成为齐次强马尔可夫过程,然后利用强马氏性及首达时间分布给出了其破产前最大盈余额与破产赤字的联合分布.     

盈余过程的马氏性与索赔到达间隔分布为离散型的连续时间风险模型

本文研究广泛的一类连续时间风险模型盈余过程的马氏性,得到了盈余过程成为马氏过程的充分必要条件．首次建立了索赔到达间隔为离散型分布的连续时间风险模型．并对两个基本特例得到了破产概率的准确表达式．     

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．     

随机利率下马氏调控Pascal模型破产概率的估计

本文研究随机环境下带随机利率的复合Pascal风险模型破产概率上界估计,对利率和费率分别按两个马氏环境变化的Pascal风险模型,给出破产概率满足的不等式.     

保费收入为Poisson过程的更新风险模型

对于保费收入为Poisson过程的更新风险模型,利用马氏链的理论,借助转移概率,得出了破产概率和破产赤字的展式及其所满足的积分方程.     

随机利率下具有马氏调控的Pascal模型

收稿研究随机环境下带利率的风险模型;对随机利率下由马氏调控费率的Pascal模型,我们克服了随机环境和随机利率的限制,得到破产概率及破产时、破产前剩余、破产赤字联合分布的计算方法.     

一类离散风险模型的盈余极值的联合分布

本文研究了一类离散风险模型,利用[1]和[2]关于古典风险模型的结论,得到了该风险过程在破产前和最后一次返回零点前公司盈余的极大值和极小值的联合分布,推广到了保费收入过程依赖于保单计数过程的情况.     

马氏环境下带扰动的Cox相关的风险模型破产概率的上界估计

本文讨论马氏环境下带随机扰动的保单数量过程与索赔次数过程Cox相关的风险模型.利用鞅方法,给出了该风险模型的破产概率的指数上界.     

马氏环境下带扰动的Cox相关的风险模型破产概率的上界估计

本文讨论马氏环境下带随机扰动的保单数量过程与索赔次数过程Cox相关的风险模型.利用鞅方 法,给出了该风险模型的破产概率的指数上界.     

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.     

Ruin probability in Sparre Andersen risk model with claim inter-arrival times distributed as Erlang

This article deals with the ruin probability in a Sparre Andersen risk process with the inter-claim times being Erlang distributed in the framework of piecewise deterministic Markov process (PDMP). We construct an exponential martingale by virtue of the extended generator of the PDMP to change the measure. Some results are derived for the ruin probabilities, such as the general expressions for ruin probability, Lundberg bounds, Cramér-Lundberg approximations, and finite-horizon ruin probability.     

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.     

马氏利率下相关险种的离散风险建模和破产概率

在随机利率服从有限齐次Markov链下,建立相关险种离散风险模型,采用递推方法得到了有限时间破产概率的递推等式和最终破产概率的积分等式;给出了有限时间破产概率和最终破产概率的上界,导出了破产时刻余额分布的计算等式.     

随机利率下双分红的变保费复合帕斯卡模型

利润最大化风险最小化是保险公司运营所追求的目标,破产概率为公司进行风险决策提供了依据。本文基于随机利率环境下,保费随公司盈余水平调整的双分红复合帕斯卡模型,研究了股份制保险公司的有限时间破产概率。我们证明了公司盈余过程的齐次马氏性,得到了有限时间破产概率的计算方法,最后给出了具体算例。     

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.