复合Poisson模型中“双界限”分红问题

引入了复合Poisson模型中的"双界限"分红模型,在这种模型中,当盈余超过上限时分红以不超过保费率的速率付出,低于下限后保费率增大.文中利用Gerber- Shiu函数来分析这种模型,先导出了Gerber-Shiu函数m_1,m_2,m_3满足的积分-微分方程,再给出m_1,m_2,m_3的解析表示,最后通过几步把Gerber-Shiu函数m(u;b_1,b)的解析式表示出来.     

一类离散相依索赔风险模型的随机分红问题北大核心CSCD

该文将随机保费收入、相依索赔以及随机分红策略引入到复合二项风险模型中,并研究该模型下的随机分红问题.运用母函数的方法,推导得到保险公司直至破产前的期望累积折现分红量满足的差分方程及其解.最后,通过几个数值例子展示了所得结果.     

带阈限分红策略的一类更新风险模型

本文考虑了索赔时间间距为Erlang(n)分布带阈限分红策略的更新风险模型的平均折现罚函数,建立了该函数所满足的积分-微分方程及更新方程,最后讨论了更新方程的解.     

保费和索赔到达率与余额相依的最优有界分红率问题

研究保费和索赔到达率与余额相依的最优有界分红问题,目标是最大化破产前的累积期望折现分红。首先,给出一个策略是平稳马氏策略的充分必要条件,运用测度值生成元的理论得到测度值动态规划方程（DPE）,并且给出了验证定理的证明。最后,讨论了测度值DPE和相应拟变分不等式（QVI）之间的关系,并且证明了最优分红策略为具有波段结构的平稳马氏策略。     

离散时间模型下带分红交易费的最优分红

研究离散Sparre-Andersen模型下带分红交易费的最优分红问题.在分红有界的条件下,通过更新初始时间得到最优值函数并证明最优值函数为Hamilton-Jacobi-Bellman方程的唯一有界解.另外,运用Bellman递推算法通过最优值变换获得最优分红.     

一类具有新红利界限的Erlang(2)风险模型

考虑到保险公司的实际运作中红利的发放率要比保费的收取率小,将一类新的红利政策引入Erlang(2)风险模型,利用更新论证,得到并求解了此模型下罚金折现期望函数所满足的微积分方程.最后通过数值例子,分析了红利界限与初始盈余对破产概率的影响.     

具有红利边界的Erlang（2）风险模型

给出了具有边界红利策略的Erlang（2）风险模型,在此红利策略下,若保险公司的盈余在红利线以下时不支付红利,否则红利以低于保费率的常速率予以支付．对于该模型,本文推导了Gerber-Shiu折现惩罚函数所满足的两个积分－微分方程和更新方程．     

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与经典Cramer-Lundberg风险模型中保费收取过程 是时间的线性函数不同, 我们考虑聚合的保费收取过程是复合Poisson过程, 研究了在此模型下的常数分红策略问题. Dickson和Waters,(2004)指出在破产发生时, 股东还应有责任偿付破产时的赤字. 因此, 在本文中考虑的最优准则是最大化破产发生前的分红折现值与破产发生时赤字的差的期望. 做为例子, 当个体保费收取额和索赔额均为指数分布时, 给出了计算分红障碍的条件     

改进后的复合Poisson-Geometric风险模型Gerber-Shiu折现惩罚函数

在考虑到因保费收入和通货膨胀等随机干扰的影响,以及将多余资本用于投资来提高赔付能力的基础上,文章对复合Poisson-Geometric风险模型做进一步推广,建立以保费收入服从复合Poisson过程,理赔量服从复合Poisson-Geometric过程的带投资的干扰风险模型,针对该风险模型,应用全期望公式,推导了Gerber-Shiu折现惩罚函数满足的更新方程,进而得到了在破产时盈余惩罚期望,破产赤字和破产概率满足的更新方程.并以保费额和索赔额均服从指数分布为例,给出破产概率满足的微分方程.以及通过数值例子,分析了初始准备金额,投资金额及保费额等对保险公司最终破产概率的影响.结论为经营者或决策者对各种金融或保险风险进行定量分析和预测提供了理论依据.     

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.     

The expected discounted penalty function under a renewal risk model with stochastic income

In this paper, we consider a renewal risk model with stochastic premiums income. We assume that the premium number process and the claim number process are a Poisson process and a generalized Erlang (n) processes, respectively. When the individual stochastic premium sizes are exponentially distributed, the Laplace transform and a defective renewal equation for the Gerber-Shiu discounted penalty function are obtained. Furthermore, the discounted joint distribution of the surplus just before ruin and the deficit at ruin is given. When the claim size distributions belong to the rational family, the explicit expression of the Gerber-Shiu discounted penalty function is derived. Finally, a specific example is provided.     

The ruin probability of the renewal model with constant interest force and upper-tailed independent heavy-tailed claims

In this paper, we obtain the uniform estimate for discounted aggregate claims in the continuous-time renewal model of upper-tailed independent and heavy-tailed random variables. With constant interest force and constant premium rate, we establish a uniform simple asymptotic formula for ruin probability of the renewal model in the case where the initial surplus is large.     

保费到达为平衡更新过程的复合更新风险模型

本文研究保费到达为平衡更新过程的复合更新风险模型 ,给出了有限时间内的生存概率分布 ,破产时间 T与破产时资产盈余 U(T)的联合分布 ,及破产时间 T与破产前瞬时盈余 U(T- )的联合分布 .     

On the expected discounted penalty functions for two classes of risk processes under a threshold dividend strategy

In this paper, the discounted penalty (Gerber-Shiu) functions for a risk model involving two independent classes of insurance risks under a threshold dividend strategy are developed. We also assume that the two claim number processes are independent Poisson and generalized Erlang (2) processes, respectively. When the surplus is above this threshold level, dividends are paid at a constant rate that does not exceed the premium rate. Two systems of integro-differential equations for discounted penalty functions are derived, based on whether the surplus is above this threshold level. Laplace transformations of the discounted penalty functions when the surplus is below the threshold level are obtained. And we also derive a system of renewal equations satisfied by the discounted penalty function with initial surplus above the threshold strategy via the Dickson-Hipp operator. Finally, analytical solutions of the two systems of integro-differential equations are presented.     

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.     

A perturbed risk model with dependence between premium rates and claim sizes

This paper considers a dependent risk model with diffusion for the surplus of an insurer, in which a current premium rate will be adjusted after a claim occurs and the adjusted rate is determined by the amount of the claim. At the same time, the diffusion is changed correspondingly. Using Rouché’s theorem, we first derive the closed-form solution for the Laplace transform of the survival probability in the dependent risk model. Then, using the Laplace transform, we derive a defective renewal equation satisfied by the survival probability. For the exponential claim sizes, we present the explicit recursion expression for the survival probability, by which we can exactly solve the survival probability step-by-step. We also illustrate the influence of the model parameters in the dependent risk model on the survival probability by numerical examples.     

A perturbed risk model with dependence between premium rates and claim sizes

This paper considers a dependent risk model with diffusion for the surplus of an insurer, in which a current premium rate will be adjusted after a claim occurs and the adjusted rate is determined by the amount of the claim. At the same time, the diffusion is changed correspondingly. Using Rouché’s theorem, we first derive the closed-form solution for the Laplace transform of the survival probability in the dependent risk model. Then, using the Laplace transform, we derive a defective renewal equation satisfied by the survival probability. For the exponential claim sizes, we present the explicit recursion expression for the survival probability, by which we can exactly solve the survival probability step-by-step. We also illustrate the influence of the model parameters in the dependent risk model on the survival probability by numerical examples.