阈红利边界下Erlang(2)风险过程的罚金折现期望函数(英文)

本文研究了阙红利边界TErlang(2)风险过程的罚金折现期望函数.利用算子变换及复合几何分布函数得到了罚金折现期望函数满足的微分积分方程,并给出了罚金折现期望函数解析表达式.     

马氏调制费率的带干扰风险模型

考虑了一类具有马氏调制的带干扰连续时间风险模型,得到了该模型下其条件Gerber-Shiu折现罚金函数所满足的积分方程,Laplace变换及渐近解.在两状态情形下,当索赔额的分布为有理数情况时得到了条件Gerber-Shiu折现罚金函数的具体表达式并给出了数值例子     

双复合泊松风险模型下的投资问题

在经典风险模型基础上,研究了保险公司保费收入和索赔均服从复合泊松过程的双复合泊松风险模型,针对最优投资策略和求解破产时刻惩罚金期望折现函数的问题,利用重期望公式和马氏性得到期望折现函数满足的带边界条件的二阶积分微分方程,通过高效的Sinc数值方法求出折现函数的近似数值解,从而由图像分析破产概率变化的趋势.     

Erlang(2)扩散风险模型的Gerber-Shiu期望折现惩罚函数

将由布朗运动刻画的随机干扰项加入到Erlang(2)风险模型中,在模型中引入了由Gerber和Shiu定义的期望折现惩罚函数,并给出了这类模型的Gerber-Shiu函数所满足的积分微分方程.     

两类索赔相关风险模型的罚金折现期望函数

考虑两类索赔相关风险模型.两类索赔计数过程分别为独立的广义Poisson过程和广义Erlang(2)过程.得到了该风险模型的罚金折现期望函数满足的积分微分方程及该函数的Laplace变换的表达式,且当索赔额均服从指数分布时,给出了罚金折现期望函数及破产概率的明确表达式.     

具有两类索赔相关风险过程的罚金折现函数

考虑两类索赔相关风险过程.两类索赔计数过程分别为独立的Poisson和广义Erlang(2)过程.将该过程转换为两类独立索赔风险过程,得到了该过程的罚金折现函数满足的积分微分方程及该函数的拉普拉斯变换的表达式,且当索赔额服从指数分布时,给出了罚金折现函数及破产概率的表达式.     

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．     

一类变保费率风险模型的Gerber-Shiu惩罚函数

本文考虑变保费风险模型,假设保费率是随时间变化的,研究了其Gerber-Shiu惩罚函数.通过无穷小方法给出 Gerber-Shiu惩罚函数所满足的积分一微分方程;在指数索赔下,给出其破产时赤字的数学期望及破产时的拉普拉斯变换.     

随机保费风险模型下的平均折现罚金函数

本文研究随机保费风险模型下与破产时刻相关的平均折现罚金函数. 与经典的Cram\'{e}r-Lundberg模型相比这里的保费过程不再是时间的线性函数, 而是一个与理赔独立的复合Possion过程. 我们得到了罚金函数所满足的积分方程, 它提供了一种研究破产量的统一方法. 利用该积分方程我们得到了破产时刻, 破产时赤字, 破产前瞬时盈余的Laplace变换; 并在指数分布的特殊情况下求出了他们的显著表达式, 推广了Boikov (2003)的结论.     

复合二项风险模型下破产概率的Pollazek-Khinchin公式

本文考虑复合二项风险模型破产概率问题,首先通过研究Gerber-Shiu折现惩罚函数,运用概率论的分析方法得到了其所满足的瑕疵更新方程,再结合离散更新方程理论研究了其渐近性质,最后,运用概率母函数的方法得到了与经典的Gramer-Lundberg模型类似的破产概率Pollazek-Khinchin公式．     

The expected discounted penalty function for the perturbed compound Poisson risk process with constant interest

In this paper, we consider the Gerber-Shiu expected discounted penalty function for the perturbed compound Poisson risk process with constant force of interest. We decompose the Gerber-Shiu function into two parts: the expected discounted penalty at ruin that is caused by a claim and the expected discounted penalty at ruin due to oscillation. We derive the integral equations and the integro-differential equations for them. By solving the integro-differential equations we get some closed form expressions for the expected discounted penalty functions under certain assumptions.     

常数分红下相依理赔量的Erlang(2)模型

该文考虑了常数障碍分红策略下的Erlang(2)模型,研究了Gerber-Shiu折现罚金函数和期望折现分红,导出了它们所满足的积分微分方程,并分析了它们的解.     

保费随机的离散风险模型的罚金期望函数

本文把经典的复合二项风险模型进行推广,其中保费收取方式不再是时间的线性函数而是一个二项过程.我们把它的罚金期望看成初始资本的函数,得到了罚金期望函数的递推公式和渐近估计,最后利用罚金期望函数的递推公式和渐近估计给出了几个重要的破产量的递推公式及其渐近估计.     

一类具有随机保费风险模型的破产问题

本文考虑了一个保费收入过程为复合Poisson过程,且索赔时间间隔分布为广义Erlang(n)分布的风险模型,给出了其罚金折现期望函数所满足的瑕疵更新方程以及渐近表达式和精确表达式.     

一类随机利率下的破产时罚金折现期望

本文在经典风险模型下, 引进带有一种随机利率的破产时罚金折现期望的概念, 其利率的随机性通过标准Wiener过程和Poisson过程来描述. 给出破产时罚金折现期望所满足的更新方程, 并利用这个更新方程给出破产时罚金折现期望的渐近公式.     

Ruin problems with stochastic premium stochastic return on investments

In this paper, ruin problems in the risk model with stochastic premium incomes and stochastic return on investments are studied. The logarithm of the asset price process is assumed to be a Lévy process. An exact expression for expected discounted penalty function is established. Lower bounds and two kinds of upper bounds for expected discounted penalty function are obtained by inductive method and martingale approach. Integro-differential equations for the expected discounted penalty function are obtained when the Lévy process is a Brownian motion with positive drift and a compound Poisson process, respectively. Some analytical examples and numerical examples are given to illustrate the upper bounds and the applications of the integro-differential equations in this paper.      

带常数边界的平衡更新风险模型的破产问题

本文讨论带常数边界的平衡更新风险模型的破产问题.利用Markov性质,给出惩罚函数满足的积分-微分方程,证明其惩罚函数可由更新风险模型的惩罚函数表示,并且给出一个具体的例子.     

On the expected discounted penalty function for the compound Poisson risk model with delayed claims

In this paper, we consider an extension to the compound Poisson risk model for which the occurrence of the claim may be delayed. Two kinds of dependent claims, main claims and by-claims, are defined, where every by-claim is induced by the main claim and may be delayed with a certain probability. Both the expected discounted penalty functions with zero initial surplus and the Laplace transforms of the expected discounted penalty functions are obtained from an integro-differential equations system. We prove that the expected discounted penalty function satisfies a defective renewal equation. An exact representation for the solution of this equation is derived through an associated compound geometric distribution, and an analytic expression for this quantity is given for when the claim amounts from both classes are exponentially distributed. Moreover, the closed form expressions for the ruin probability and the distribution function of the surplus before ruin are obtained. We prove that the ruin probability for this risk model decreases as the probability of the delay of by-claims increases. Finally, numerical results are also provided to illustrate the applicability of our main result and the impact of the delay of by-claims on the expected discounted penalty functions.