马氏调制费率复合Poisson-Geometric风险模型的预警区问题

考虑了一类具有马氏调制费率的复合Poisson-Geometric过程风险模型,充分利用盈余过程的强马氏性,得到第一个预警区的一个条件矩母函数所满足的微积分方程,并进一步在两状态情形下,当理赔额的分布为指数分布时得到了第一个预警区的一个条件矩母函数的具体表达式以解释结果.需要特别指出的是,所研究模型的盈余过程不具有平稳增量性,只能充分运用盈余过程的强马氏性,研究了一类具有马氏调制费率的复合Poisson-Geometric过程风险模型的预警区问题,丰富了保险公司对预警区问题的研究,对保险公司考虑财务预警系统以及保险监管部门设计某些监管指标系统具有一定的参考指导价值.     

复合Poisson-Geometric风险模型的预警区问题

应用有别于传统鞅方法的方法,充分利用盈余过程的强马氏性,在一类复合Poisson-Geometric风险模型下讨论预警区问题,得到第一个预警区的一个条件矩母函数所满足的微积分方程,并在指数索赔情形下给出其精确解.     

DURATION OF NEGATIVE SURPLUS FOR A TWO STATE MARKOV-MODULATED RISK MODEL

We consider a continuous time risk model based on a two state Markov process, in which after an exponentially distributed time, the claim frequency changes to a different level and can change back again in the same way. We derive the Laplace transform for the first passage time to surplus zero from a given negative surplus and for the duration of negative surplus. Closed-form expressions are given in the case of exponential individual claim. Finally, numerical results are provided to show how to estimate the moments of duration of negative surplus.     

常利率复合Poisson风险模型中的预警区问题

该文讨论了带常利率复合Poisson风险模型中的预警区问题.在此,作者提出了一种新的方法,其有别于Gerber于1990年提出的鞅方法,通过这种新方法,最终得到了负盈余持续时间的矩母函数及各阶矩,进而在索赔指数情形给出了精确解析式,并利用计算得到的数值结果讨论了利率变化对预警区的影响.     

一类推广的常利率复合Poisson-Geometric风险模型的预警区问题

在复合Poisson-Geometric风险模型的基础上,引入利率因素,并将保费收入由线性过程推广为复合Poisson过程,建立了一类推广的带常利率复合Poisson-Geometric风险模型,该模型描述现实的能力更强,更具有实际意义.然后,利用盈余过程的强马氏性推导出了首个预警区的条件矩母函数所满足的积分方程,并进一步在保费额和索赔额都服从指数分布的情形下得出了其解析解.     

关于古典风险模型的一个联合分布

本文主要讨论古典风险模型矿产瞬间前的余额，破产时的赤字，破产前的最大余额，最后一次破产前的最大余额等的联合分布。     

Total duration of negative surplus for the dual model

In the dual model, we allow the surplus process to continue if the surplus falls below zero. By introducing the renewal measure of the defective renewal sequence constituted by the zero points of the surplus process, we obtain the probability of hitting the zero point. Further, we derive formulae for the Laplace transform, expectation and variance of total duration of negative surplus and present some examples with an exponential individual jump amount distribution. Copyright © 2008 John Wiley & Sons, Ltd.     

Markov-modulated风险模型中盈余过程零点数的分布

基于保险公司在首次破产后仍能继续运转的情形,讨论并得到了Markovmodulated风险模型中盈余过程零点数的分布.     

Markov-Modulated风险模型的极大值、极小值及零点数的联合分布

本文基于保险公司在首次破产后仍能继续运转的情形,讨论并得到了Markov-modulated风险模型中关于末离零点前盈余过程极大值、极小值及零点数的联合分布.     

Total duration of negative surplus for a MAP risk model

In this paper, we study the risk model with Markovian arrivals where we allow the surplus process to continue if the surplus falls below zeroWe first derive expressions for the severity of ruinThen by using the strong Markovian property of a two-dimensional Markov process and the expression for the severity of ruin, we obtain the Laplace transform of the total duration of negative surplus.     

具有两种副索赔的离散相依风险模型破产问题

考虑了一类离散相依的风险模型,该模型假设主索赔以一定的概率引起两种副索赔,而第一种副索赔有可能延迟发生.通过引入一个辅助模型,分别得出了该风险模型初始盈余为0时破产前盈余与破产时赤字的联合分布的表达式、初始盈余为"时破产前盈余和破产时赤字的联合分布的递推公式、初始盈余为0时的破产概率,以及初始盈余为"时的破产概率求解方...     

Joint distributions of some actuarial random vectors for the Cox risk model

The main purpose of this paper was to investigate the joint distributions of some actuarial vectors that contain the ruin time for the Cox risk model. Joint distributions of some actuarial vectors such as those containing the ruin time, the maximum surplus before ruin, duration of the surplus being negative, and others are important for measuring the risk management level and the severity caused by ruin. In the past decade, great literatures have devoted to the study of these distributions for classical models, such as the compound Poisson model and the perturbed compound Poisson model etc. The main result of this paper provides the joint distributions of these actuarial vectors for the Cox risk model—a model with wide applications in risk theory. The main method of this paper is to apply the idea of ‘operational time scale’ to the Cox model, which enables us to solve our problem by intergrading some existing results for the compound Poisson risk model. To some extent, we can view our work as an extension of joint distributions of some actuarial vectors for the compound Poisson risk model to the ones for the Cox risk model. Copyright © 2011 John Wiley & Sons, Ltd.     

利率相依的离散时间保险风险模型的破产问题

本文对利率具有一阶自回归的离散时间风险模型进行了研究,得到了破产前最大盈余的分布,破产前盈余、破产后赤字与破产前最大盈余的联合分布以及首达某一水平x的时间分布的递推公式.     

Total duration of negative surplus for a Brownian motion risk model with interest

In this paper,we consider the Brownian motion risk model with interest.The Laplace transform of the first exit time from the upper barrier before hitting the lower barrier is obtained.Using the obtained result and exploiting the limitation idea,we derive the Laplace transform of total duration of negative surplus.     

离散时间模型下最大赤字问题

本文对引入利率的离散时间风险模型得到了破产前最大盈余的分布 ,破产前盈余、破产后赤字与破产前最大盈余的联合分布以及首达某一水平 x的时间分布的递推公式 ,对不带利率的模型得到了最大赤字、发生最大赤字的时间的分布     

Stochastic analysis of life insurance surplus

The aim of the paper is to examine the behavior of insurance surplus over time for a portfolio of homogeneous life policies. We distinguish between stochastic and accounting surpluses and derive their first two moments. A recursive formula is proposed for calculating the distribution function of the accounting surplus. We then examine the probability that the accounting surplus becomes negative in a given insurance year. Numerical examples illustrate the results for portfolios of temporary and endowment life policies assuming a conditional AR(1) process for the rates of return.     

On the time value of absolute ruin with tax

Consider a compound Poisson surplus process of an insurer with debit interest and tax payments. When the portfolio is in a profitable situation, the insurer may pay a certain proportion of the premium income as tax payments. When the portfolio is below zero, the insurer could borrow money at a debit interest rate to continue his/her business. Meanwhile, the insurer will repay the debts from his/her premium income. The negative surplus may return to a positive level except that the surplus is below a certain critical level. In the latter case, we say that absolute ruin occurs. In this paper, we discuss absolute ruin quantities by defining an expected discounted penalty function at absolute ruin. First, a system of integro-differential equations satisfied by the expected discounted penalty function is derived. Second, closed-form expressions for the expected discounted total sum of tax payments until absolute ruin and the Laplace-Stieltjes transform (LST) of the total duration of negative surplus are obtained. Third, for exponential individual claims, closed-form expressions for the absolute ruin probability, the LST of the time to absolute ruin, the distribution function of the deficit at absolute ruin and the expected accumulated discounted tax are given. Fourth, for general individual claim distributions, when the initial surplus goes to infinity, we show that the ratio of the absolute ruin probability with tax to that without tax goes to a positive constant which is greater than one. Finally, we investigate the asymptotic behavior of the absolute ruin probability of a modified risk model where the interest rate on a positive surplus is involved.     

一类推广的复合Poisson-Geometric风险模型下预警区问题的研究

该文研究一类推广的复合Poisson-Geometric风险模型的预警区问题,此模型保费收入过程是复合Poisson过程, 索赔次数过程是复合Poisson-Geometric过程. 充分利用盈余过程的强马氏性和全期望公式,得到了赤字分布的积分表达式, 进而得到了单个预警区和总体预警区的矩母函数的表达式.     

Parisian ruin with a threshold dividend strategy under the dual Lévy risk model

We consider the threshold dividend strategy where a company’s surplus process is described by the dual Lévy risk model. Namely, the company chooses to pay dividends at a constant rate only when the surplus is above some nonnegative threshold. Classically, such a company is referred to be ruined immediately when the surplus level becomes negative. Recently, researchers investigate the Parisian ruin problem where the company is allowed to operate under negative surplus for a predetermined period known as the Parisian delay. With the help of the fluctuation identities of spectrally negative Lévy processes, we obtain an explicit expression of the expected discounted dividends until Parisian ruin in terms of the relevant scale functions and certain probabilities that need to be evaluated for each specific Lévy process. The optimal threshold level under such a threshold dividend strategy is deduced. Applications and numerical examples are given to illustrate the theoretical results and examine how the expected discounted aggregate dividends and the optimal threshold level change in response to different Parisian delays.     

离散的相依风险模型的破产问题

研究一类索赔时间相依的离散风险模型,模型中假设每次主索赔可能引起一次副索赔,而每次副索赔有可能延迟发生.通过引入辅助模型,运用概率论的分析方法得到了破产前瞬时盈余和破产时赤字联合分布的递推解,以及初始值为0时最终破产概率的明确表达式.最后结合保险实例进行了数值模拟.