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.     

支付红利的复合二项模型

本文在完全离散的复合二项经典风险模型的基础上,考虑随机地支付红利的模型,当盈余大于或等于一个给定的非负整数红利界,并且没有索赔发生时,保险公司就以概率q0支付一个单位的红利,本文获得了这个模型的破产概率、破产时赤字的分布等的递推公式.     

相依索赔的二项风险模型的Gerber-shiu贴现罚函数

研究一类索赔时间相依的二项风险模型,根据索赔额的大小随机产生一副索赔.通过引入辅助模型,运用概率论的分析方法得到了任意初始值μ下的Gerber-Shiu贴现罚函数,并求得了初始值为0时最终破产概率的明确表达式.最后结合保险实务进行了举例.     

一类索赔相依二元风险模型的破产概率问题研究

考虑一种相依索赔风险模型,模型中假设每次主索赔可随机产生一延迟的副索赔,采用Laplacc变换方法,给出了索赔额服从轻尾分布时的最终破产概率,并研究了重尾分布时最终破产概率的渐进式.     

双二项风险模型的破产概率

首先将经典的复合二项风险模型推广到保费到达过程与个体索赔过程是两个相互独立的二项过程的一种新模型，然后运用两种方法得出破产概率满足的一般公式和Lundberg不等式．     

完全离散复合二项风险模型破产概率的一个新求法

本文主要利用过程的马尔可夫性对完全离散复合二项风险模型进行研究,首先得到了赔付间断时间序列和赔付时刻赢余的有限维联合密度,然后根据这一结论,得到了新的破产概率公式以及有限时间内的生存概率公式,并在当初始资本u=0,c=1,赔付随机变量服从赌徒分布即P(Yi=2)=1,i=1,2,3,…的情况下,得到了有限时间内的生存概率.     

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.     

一类相依索赔风险模型的破产概率问题研究

考虑一种相依索赔风险模型,其中每次索赔发生时根据索赔额的大小可随机产生一延迟的副索赔.采用L ap lace变换方法,给出了索赔额服从轻尾分布时的最终破产概率,并研究了重尾分布时最终破产概率的极限上下界.     

离散随机序在复合二项破产模型中的应用

本文的内容由三部分组成 .首先 ,在简述复合二项破产模型近期已得的相关成果的基础上 ,给出了最终破产概率的复合几何分布表示 ;接着 ,在概述了离散随机优序与停止损失序的主要结果后 ,首次提出了幂序的概念 ;最后 ,借助上述离散随机序 ,在复合二项破产模型中探讨了个体索赔额对于最终破产概率与调节系数的影响     

On the first time of ruin in the bivariate compound Poisson model

This paper considers a bivariate compound Poisson model for a book of two dependent classes of insurance business. We focus on the ruin probability that at least one class of business will get ruined. As expected, general explicit expressions for this bivariate ruin probability is very difficult to obtain. In view of this, we introduce the so-called bivariate compound binomial model which can be used to approximate the finite-time survival probability of the assumed model. We then study some simple bounds for the infinite-time ruin probability via the association properties of the bivariate compound Poisson model. We also investigate the impact of dependence on the infinite-time ruin probability by means of multivariate stochastic orders.     

Ruin probability and joint distributions of some actuarial random vectors in the compound pascal model

The compound negative binomial model,introduced in this paper,is a discrete time version.We discuss the Markov properties of the surplus process,and study the ruin probability and the joint distributions of actuarial random vectors in this model.By the strong Markov property and the mass function of a defective renewal sequence,we obtain the explicit expressions of the ruin probability,the finite-horizon ruin probability,the joint distributions of T,U(T-1),|U(T)| and 0≤inn相似文献   

Finite-horizon ruin probability asymptotics in the compound discrete-time risk model

In this paper, we consider the compound discrete-time risk model which is a modification of the classical discrete-time (compound binomial) risk model. In this model, the claims in each fixed subsequent time interval arrive independently, and their number is random. We find the asymptotics of finite-horizon ruin probability in such a model for a subclass of heavy-tailed claim sizes and claim numbers.     

EXPECTED PRESENT VALUE OF TOTAL DIVIDENDS IN THE COMPOUND BINOMIAL MODEL WITH DELAYED CLAIMS AND RANDOM INCOME

In this paper, a compound binomial model with a constant dividend barrier and random income is considered. Two types of individual claims, main claims and by-claims, are defined, where every by-claim is induced by the main claim and may be delayed for one time period with a certain probability. The premium income is assumed to another binomial process to capture the uncertainty of the customer＇s arrivals and payments. A system of difference equations with certain boundary conditions for the expected present value of total dividend payments prior to ruin is derived and solved. Explicit results are obtained when the claim sizes are Kn distributed or the claim size distributions have finite support. Numerical results are also provided to illustrate the impact of the delay of by-claims on the expected present value of dividends.     

Expected present value of total dividends in a delayed claims risk model under stochastic interest rates

In this paper, a compound binomial risk model with a constant dividend barrier under stochastic interest rates is considered. Two types of individual claims, main claims and by-claims, are defined, where every by-claim is induced by the main claim and may be delayed for one time period with a certain probability. In the evaluation of the expected present value of dividends, the interest rates are assumed to follow a Markov chain with finite state space. A system of difference equations with certain boundary conditions for the expected present value of total dividend payments prior to ruin is derived and solved. Explicit results are obtained when the claim sizes are K_n distributed or the claim size distributions have finite support. Numerical results are also provided to illustrate the impact of the delay of by-claims on the expected present value of dividends.     

连续时间复合二项模型多维精算量的联合分布

连续时间复合二项模型是由文献首先提出的.作为离散时间复合二项模型的连续化版本,连续时间复合二项模型的极限形式即为经典风险模型.为了得到该模型多维精算量的联合分布,该文引入了一列上穿零点,推导出该列上穿零点所构成的缺陷(defective)更新序列的更新质量函数.利用此更新质量函数及余额过程的强马氏性可以得到破产概率和包含破产时间,破产前余额,破产严重程度,破产前最大盈余,破产到恢复的最大赤字,整个过程的最大赤字等多维精算量的联合分布.由此联合分布得到其1-骨架链—离散时间复合二项模型的对应的联合分布,最后给出在1-骨架链中索赔额服从指数分布时这一特殊情况下相应多维精算量的联合分布的明确表达式.     

一类广义双险种二项风险模型的破产概率

讨论了双险种的一般情形的二项风险模型,得到了其破产概率的一般公式和Lundberg不等式.     

The Compound Poisson Surplus Model with Interest and Liquid Reserves: Analysis of the Gerber–Shiu Discounted Penalty Function

We modify the compound Poisson surplus model for an insurer by including liquid reserves and interest on the surplus. When the surplus of an insurer is below a fixed level, the surplus is kept as liquid reserves, which do not earn interest. When the surplus attains the level, the excess of the surplus over the level will receive interest at a constant rate. If the level goes to infinity, the modified model is reduced to the classical compound Poisson risk model. If the level is set to zero, the modified model becomes the compound Poisson risk model with interest. We study ruin probability and other quantities related to ruin in the modified compound Poisson surplus model by the Gerber–Shiu function and discuss the impact of interest and liquid reserves on the ruin probability, the deficit at ruin, and other ruin quantities. First, we derive a system of integro-differential equations for the Gerber–Shiu function. By solving the system of equations, we obtain the general solution for the Gerber–Shiu function. Then, we give the exact solutions for the Gerber–Shiu function when the initial surplus is equal to the liquid reserve level or equal to zero. These solutions are the key to the exact solution for the Gerber–Shiu function in general cases. As applications, we derive the exact solution for the zero discounted Gerber–Shiu function when claim sizes are exponentially distributed and the exact solution for the ruin probability when claim sizes have Erlang(2) distributions. Finally, we use numerical examples to illustrate the impact of interest and liquid reserves on the ruin probability.      

Ruin probabilities in the discrete time renewal risk model

In this paper, we study the discrete time renewal risk model, an extension to Gerber’s compound binomial model. Under the framework of this extension, we study the aggregate claim amount process and both finite-time and infinite-time ruin probabilities. For completeness, we derive an upper bound and an asymptotic expression for the infinite-time ruin probabilities in this risk model. Also, we demonstrate that the proposed extension can be used to approximate the continuous time renewal risk model (also known as the Sparre Andersen risk model) as Gerber’s compound binomial model has been proposed as a discrete-time version of the classical compound Poisson risk model. This allows us to derive both numerical upper and lower bounds for the infinite-time ruin probabilities defined in the continuous time risk model from their equivalents under the discrete time renewal risk model. Finally, the numerical algorithm proposed to compute infinite-time ruin probabilities in the discrete time renewal risk model is also applied in some of its extensions.     

复合二项风险模型下Gerber-Shiu折现惩罚函数的渐近解

首先研究了二项风险模型下Gerber-Shiu折现惩罚函数所满足的瑕疵更新方程,然后根据离散更新方程理论研究了其渐近解,并得到了破产概率、破产即刻前赢余和破产时刻赤字的联合分布分布以及其边际分布等的渐近解,进一步完善了Pavlova K P和Willmot G E 2004年发表的相关问题的结果.     

Estimates for the ruin probability of a time-dependent renewal risk model with dependent by-claims

Consider a continuous-time renewal risk model, in which every main claim induces a delayed by-claim. Assume that the main claim sizes and the inter-arrival times form a sequence of identically distributed random pairs, with each pair obeying a dependence structure, and so do the by-claim sizes and the delay times. Supposing that the main claim sizes with by-claim sizes form a sequence of dependent random variables with dominatedly varying tails, asymptotic estimates for the ruin probability of the surplus process are investigated, by establishing a weakly asymptotic formula, as the initial surplus tends to infinity.