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.     

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本文讨论了信用衍生产品之一的总收益互换的定价问题. 其中涉及到利率风险和违约风险, 本文利用HJM利率模型来刻画利率风险, 并利用强度模型和混合模型对违约风险进行建模. 分别考虑了违约时间与利率无关时总收益互换合约的定价问题, 以及违约时间与利率相关时总收益互换合约的定价问题, 给出了相应的定价模型, 并用蒙特卡罗模拟方法得到定价问题的数值解.     

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.     

基于违约风险的Vasicek利率风险研究

本文将非瞬时利率作为状态变量,通过Vasicek双因素期限结构模型得到了随机久期和凸度,并且讨论了考虑违约风险的Vasicek随机久期和凸度,使得对债券进行投资时,用Vasicek模型进行利率风险管理更加符合实际情况。     

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.     

债券定价及利率风险的市场价格的重构方法

假设利率变化的模型是由随机微分方程给出,则可以用推导Black-Scholes方程的方法来推出债券价格满足的偏微分方程,得到一个抛物型的偏微分方程.但是,在债券定价的方程中隐含有一个参数λ称为利率风险的市场价格.所谓债券定价的反问题,就是由不同到期时间的债券的现在价格来得到利率风险的市场价格.对随机利率模型下债券定价的正问题先给予介绍和差分数值求解方法,并介绍了反问题,且对反问题给出了数值方法.     

基于分数维Vasicek利率模型的CDS定价

本文研究CDS的定价问题, 其中涉及到利率风险和传染风险. 文中用分数维Vasicek利率模型刻画利率风险, 对公司的违约强度进行建模, 给出了违约与利率相关时风险债券的价格, 并在此基础上得到CDS的价格.     

常利率复合二项双险种风险模型的研究

提出了含利率因素的复合二项双险种风险模型,并在有关假设的基础上,给出了此模型下保险公司稳定经营的必要条件;证明了索赔时刻的盈余过程是一马氏过程和调节系数的存在性,并采用递归方法得到了模型的破产概率的上界估计.     

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.     

利率为马氏链的离散时间风险模型的破产概率(英文)

本文考虑了带随机利率的离散时间风险模型.在假设利率为马氏链条件下,得到了有限时间和最终破产概率所满足的递推积分方程,以及最终破产概率的Lundberg不等式.     

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.     

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.     

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.     

The Asymptotic Estimate of Absolute Ruin Probabilities in the Renewal Risk Model with Constant Force of Interest

In this paper, absolute ruin problems for a kind of renewal risk model with constant interest force are studied. For certain situations of the claim distribution with heavy tail, consider the surplus of the arrival time, and discrete the surplus process, then use the method of renewal function and convolution, we present the asymptotic properties of absolute ruin probability when the initial surplus tends to infinity.     

On the Distribution of Duration of First Negative Surplus for a Discrete Time Risk Model with Random Interest Rate

In this paper, we examine further annuity-due risk model presented by Cai (Probability in the Engineering and Informational Sciences, 16(2002), 309-324). We consider the computation for the distribution of duration of first negative surplus and the algorithm is shown for calculating probability that ruin occurs and the duration of first negative surplus takes any nonnegative integers values. Numerical illustration for the main result is given.     

基于监管的保险公司最优比例再保险策略

根据监管规定,保险公司必须提存一定水平的准备金.鉴于此,保险公司必须保持盈余不低于这个准备金水平.将保险公司盈余首达该准备金水平的时刻定义为``破产"时刻,以最小化``破产"概率为目标;假设保险公司可购买比例再保险, 其盈余过程由扩散模型刻画且盈余按连续复利方式计算利息, 其中利力为常数; 借助随机动态规划方法, 通过求解相应的HJB方程得到了最优值函数与最优比例再保险策略的解析式. 最后给出了经济解释与数值算例.     

关于常利率风险模型在破产前后余额的分布

本文对常利率风险模型运用拉普拉斯变换给出了破产前后余额通过破产概率函数表示的有限公式,以及破产概率的分析表达式,另外对于破产前后余额分布的密度与破产前余额密度之间关系简要说明。