基于二项分布的短期聚合风险模型

重点讨论了索赔次数服从于二项分布的情况下单个险种和多个险种的聚合风险模型,得出了在此情况下求其分布函数的若干方法,并给出聚合理赔量的两种近似模型,正态近似和平移伽马近似.最后给出了一个数值例子,验证了本文的分布函数的若干求法.     

聚合风险模型下Esscher风险度量的估计及其大样本性质

Esscher度量是一种重要的风险度量,在金融风险管理、保险精算中有广泛的应用,然而大部分关于Esscher风险度量的文献均在个体风险模型下考虑的.本文建立了聚合风险模型下Esscher度量的估计模型,得到了相应的非参数估计,并证明了估计的强相合性和渐近正态性,最后,通过数值模拟的方法验证了估计的大样本性质.     

基于污染Gamma分布的聚合风险模型及其在风险分类中的应用

分析了污染Gamma分布及其性质,讨论了基于污染Gamma分布的聚合风险模型.对模型的概率特性和参数估计进行了分析,并对该模型在风险分类中的应用进行了讨论.为克服索赔总量的分布函数在计算上的困难,利用同单调性理论得到了随机凸序意义下索赔总量随机变量S的随机上界Sc,对Sc的分布函数及限额损失保费进行了讨论.通过一个例子对所述结论的有效性进行验证.     

相依风险模型下风险保费的信度估计

建立了风险之间呈现某种特殊相依结构的信度模型.利用正交投影的方法,得到了相依风险模型下的Bühlmann信度保费和Bühlmann-Straub信度保费,并讨论了信度估计的统计性质.结论表明,在风险之间呈现相依结构时,信度预测是个体索赔均值,总索赔均值和聚合保费三者的加权和,从而推广了经典的信度理论.     

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.     

一种多目标条件风险值数学模型

研究了一种多目标条件风险值(CVaR)数学模型理论.先定义了一种多目标损失函数下的α-VaR和α-CVaR值,给出了多目标CVaR最优化模型.然后证明了多目标意义下的α-VaR和α-CVaR值的等价定理,并且给出了对于多目标损失函数的条件风险值的一致性度量性质.最后,给出了多目标CVaR模型的近似求解模型.     

有风险控制的最优投资组合(英)

本文讨论有风险控制的最优投资组合问题并研究了倍率风险函数及临界风险的性质,最大最小风险的估计;给出了其倍率风险函数有严格解析形式的例子．     

竞争型二元风险模型破产概率

本文研究了竞争型的二元风险模型,定义了两类破产概率以及状态过程,利用经典风险模型的已有结果和条件期望的性质,得到两类破产概率表达式,以及单个保险公司有限时间破产概率和最终破产概率,并给出两个保险公司的状态过程的概率分布列.     

基于均值和CVaR的效用最大化模型研究

本文利用CVaR方法代替方差或VaR来度量风险,建立了关于期望和CVaR的效用最大化模型,研究了n种风险资产的投资决策问题。在效用函数是凹的假设下,首先得到了无差异曲线的特征及均值-CVaR模型有效边界的性质,然后利用这些结论得到了效用最大值存在的条件及其最优解的性质特征,给出了求解的具体步骤和算法,并分析了最大效用点的经济含义.最后,一个基于中国股票市场真实数据的数值算例说明了本文的结论及应用。     

相依样本下半参数变系数期望分位数风险度量模型统计推断

本文在α-混合序列假设下,基于半参数变系数模型研究条件期望分位数风险价值(expectile-based value at risk, EVaR)的风险度量.此模型不仅考虑了风险因素的影响,还可以动态描述风险影响及交互效应.同时, EVaR比经典的风险在险价值(quantile-based value at risk, QVaR)具有更直观、更易于计算的良好性质,而且对于资产分布的尾部损失更加敏感,在度量极端风险情形下,相对于QVaR更为有效和方便.本文采用三阶段估计的方法,分别对变系数部分和常系数部分的参数进行估计,并且给出3个阶段中每个估计的相合性和渐近正态性.为了节省计算时间,提高计算效率,本文采用一步估计的算法,减少迭代所需的时间.由于时间序列样本是非独立样本,建立这些统计量的大样本性质时带来了更大的困难.有别于独立同分布的观察数据,本文利用大小块分割方法发展α-混合序列的极限理论,获得了基于金融时间序列数据建立的模型参数和非参数估计的统计渐近性质.在数值模拟中,本文给出3个模型假设下变系数曲线估计和常系数估计的结果,无论是估计的精确度还是估计的稳健性,模拟结果都表明本文所提出的估计方法有优良的性质.实例则展示了本文所提出模型在上证指数的实际应用.     

Calculation of the probability of eventual ruin by Beekman's convolution series

This paper presents an algorithm for evaluating the probability of eventual ruin in a collective risk model. The method is based on Beekman's convolution series for the ruin probability. It is assumed that the claim number process is Poisson and the individual claim amounts take on integer values only.     

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.     

Optimal investment policy of an insurance firm

In this paper we consider an investment problem by an insurance firm. As in the classical model of collective risk, it is assumed that premium payments are received deterministically from policyholders at a constant rate, while the claim process is determined by a compound Poisson process. We introduce a conversion mechanism of funds from cash into investments and vice versa. Contrary to the conventional collective risk model we do not assume a ruin barrier. Instead we introduce conversion costs to account for the problems implicit in reaching the zero boundary. The objective of the firm is to maximize its net profit by selecting an appropriate investment strategy. A diffusion approximation is suggested in order to obtain tractable results for a general claim size distribution.     

古典风险模型下的绝对破产

在古典绝对破产模型下盈余过程为是逐段决定马尔可夫过程.根据逐段决定马尔可夫过程具有马氏性和强马氏性,本文推导出了在古典风险模型下绝对破产概率的一个明确表达式.     

Risk aggregation in multivariate dependent Pareto distributions

In this paper we obtain closed expressions for the probability distribution function of aggregated risks with multivariate dependent Pareto distributions. We work with the dependent multivariate Pareto type II proposed by Arnold (1983, 2015), which is widely used in insurance and risk analysis. We begin with an individual risk model, where the probability density function corresponds to a second kind beta distribution, obtaining the VaR, TVaR and several other tail risk measures. Then, we consider a collective risk model based on dependence, where several general properties are studied. We study in detail some relevant collective models with Poisson, negative binomial and logarithmic distributions as primary distributions. In the collective Pareto–Poisson model, the probability density function is a function of the Kummer confluent hypergeometric function, and the density of the Pareto–negative binomial is a function of the Gauss hypergeometric function. Using data based on one-year vehicle insurance policies taken out in 2004–2005 (Jong and Heller, 2008) we conclude that our collective dependent models outperform other collective models considered in the actuarial literature in terms of AIC and CAIC statistics.     

Ruin probabilities for a risk model with two classes of claims

In this paper we consider a risk model with two kinds of claims, whose claims number processes are Poisson process and ordinary renewal process respectively. For this model, the surplus process is not Markovian, however, it can be Markovianized by introducing a supplementary process, We prove the Markov property of the related vector processes. Because such obtained processes belong to the class of the so-called piecewise-deterministic Markov process, the extended infinitesimal generator is derived, exponential martingale for the risk process is studied. The exponential bound of ruin probability in iafinite time horizon is obtained.     

一类带干扰的多险种风险模型

本文考虑一类带干扰的两独立险种的风险模型,其中两索赔次数过程分别为Poisson过程和Elang(2)过程.主要得出该模型的生存概率所满足的积分-微分方程和破产概率的渐近性.     

Collective risk models with dependence

In actuarial science, collective risk models, in which the aggregate claim amount of a portfolio is defined in terms of random sums, play a crucial role. In these models, it is common to assume that the number of claims and their amounts are independent, even if this might not always be the case. We consider collective risk models with different dependence structures. Due to the importance of such risk models in an actuarial setting, we first investigate a collective risk model with dependence involving the family of multivariate mixed Erlang distributions. Other models based on mixtures involving bivariate and multivariate copulas in a more general setting are then presented. These different structures allow to link the number of claims to each claim amount, and to quantify the aggregate claim loss. Then, we use Archimedean and hierarchical Archimedean copulas in collective risk models, to model the dependence between the claim number random variable and the claim amount random variables involved in the random sum. Such dependence structures allow us to derive a computational methodology for the assessment of the aggregate claim amount. While being very flexible, this methodology is easy to implement, and can easily fit more complicated hierarchical structures.     

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.