Finite-time ruin probability with NQD dominated varying-tailed claims and NLOD inter-arrival times

In 2007, Chen and Ng investigated infinite-time ruin probability with constant interest force and negatively quadrant dependent and extended regularly varying-tailed claims. Following this work, the authors obtain a weakly asymptotic equivalent formula for the finite-time and infinite-time ruin probability with constant interest force, negatively quadrant dependent, and dominated varying-tailed claims and negatively lower orthant dependent inter-arrival times. In particular, when the claims are consistently varying-tailed, an asymptotic equivalent formula is presented. This research is supported by the National Science Foundation of China under Grant No. 10671139.     

基于参数化分位回归模型的非寿险准备金评估

准备金及其风险边际对保险公司的偿付能力具有决定性影响.均值回归模型在非寿险准备金评估中的应用较为普遍,但需要通过Bootstrap等方法计算准备金的风险边际.分位回归模型可以一次性求得准备金及其风险边际的预测值,所以在非寿险准备金评估中具有独特的应用价值.基于GB2(Generalized Beta type 2)分布建立了一种参数化分位回归模型,该模型首先对GB2分布中的位置参数和尺度参数同时引入流量三角形数据中的事故年和进展年作为解释变量,增加了模型的灵活性;其次,根据模型参数的极大似然估计结果,借助分位数函数的表达式,计算了不同分位数水平下的准备金预测值;最后,利用极大似然估计的渐近性质,通过Delta方法给出了准备金预测值的误差.基于一组增量赔款数据的实证研究结果表明,GB2参数化分位回归模型在非寿险准备金评估及其风险边际的预测中具有良好的应用价值.     

先验与后验相结合的汽车保险索赔模型

在传统的汽车定价中,建立索赔模型通常使用后验经验估费法,这种后验方法因为忽略重要的先验信息而存在缺陷。本文提出了先验与后验方法相结合的新索赔模型,并使用信度理论对新老模型进行比较分析,最后给出了具体计算方法和实例。研究表明,新索赔模型不仅使车险定价更公平合理,降低定价风险;而且易于运用。     

Ruin probabilities with pairwise quasi-asymptotically independent and dominatedly-varying tailed claims

This paper considers the nonstandard renewal risk model in which a part of surplus is invested into a Black-Scholes market whose price process is modelled by a geometric Brownian motion, claim sizes form a sequence of not necessarily identically distributed and pairwise quasi-asymptotically independent random variables with dominatedly-varying tails.The authors obtain a weakly asymptotic formula for the finite-time and infinite-time ruin probabilities.In particular,if the claims are identically distributed and consistently-varying tailed,then an asymptotic formula is presented.     

两类相关索赔模型下破产概率的若干结果

研究了两类相关风险模型中生存概率φ(u)的问题,将其中一个风险由一个复合Poisson过程推广到了广义复合Poisson过程,求出了索赔额分布为指数分布时生存概率的明确表达式,并研究了此模型下索赔额分布重尾时,φ(u)的一个尾等价关系.     

考虑用户风险规避的V2G备用消费价格补贴CVaR模型研究

在单风险中性电网公司与单风险规避用户组成的V2G备用销售侧系统中,用户的风险规避及电网公司对其的消费价格补贴都会直接影响用户备用预订和消费行为.在CVaR风险度量准则下,构建了考虑用户风险规避的V2G备用消费价格补贴CVaR模型,并分别求解了一体化和分散决策下有、无消费价格补贴时的用户最优备用预订容量,以及有消费价格补贴下电网公司的均衡消费价格补贴.在此基础上,给出了利用消费价格补贴协调该V2G备用销售侧系统且达到Pareto改进时用户风险规避程度、电网公司备用预订合约价格以及消费价格补贴之间满足的解析关系.最后,将模型拓展到双方考虑用户风险规避信息不对称,分析用户隐瞒风险规避程度的动机及其对有消费价格补贴下的分散决策CVaR模型的影响.研究发现:在消费价格补贴策略下,风险规避型用户的最优V2G备用预订容量与其风险规避值负相关,而与备用预订的合约价格正相关;用户的风险规避值会对其均衡时的CVaR利润产生先负向后正向的影响;在电网公司与用户对后者风险规避程度存在信息不对称的情形下,用户为了提高获得的最优CVaR利润,具有虚假报高风险规避值的动机.数值算例也验证了所提出的模型与理论分析的可行性.     

THE ALGEBRAIC CRITERIA FOR THE ASYMPTOTIC BEHAVIOR OF COOPERATIVE SYSTEMS WITH CONCAVE NONLINEARITIES

For the discrete dynamical system on the nonnegative orthant generated bya cooperative and concave map T, we present an algebraic criterion of its asymptoticbehavior. The global behavior of such a system is completely determined by the sign of allprincipal minors of the matrix I-DT(0). This criterion applies to the cooperative systemwhich is concave, time-dependent and periodic in t. We give the sufficient conditions thatthe zero solution of such a system is globally asymptotically stable and that it possesses anonzero periodic solution which attracts all initial conditions in the nonnegative orthant.except at the origin. The results of Smith under weaker conditions and some applicationsare included.     

基于信息不对称的银行信贷风险决策机制及分析(Ⅰ)——信贷风险决策模型

研究商业银行在信息不对称的信货市场中 ,当存在高、低两种不同风险类型的贷款企业时 ,银行因无法准确判断企业投资项目的风险类型 ,因而造成了信贷资金的损失或机会损失 .分析并研究了这两种损失常见的几种情形及其数学原理 ,建立了银行信贷风险的决策模型 ,给出其 Kuhn-Tucker条件 .指出了在模型之下 ,当抵押品作为鉴别企业风险类型的手段失效时 ,为规避信贷风险 ,银行对企业提供的抵押品价值将有特殊的要求 .     

不完全市场上一种未定权益的套期保值策略

在标的资产价格服从几何布朗运动的Black-Scholes模型中，金融市场为完全市场时，给出一种精确的套期保值策略，然后在不完全市场引入一种动态的风险度量准则，在风险中性的概率测度诱导的金融市场上。对一种未定权益找到了在风险的动态度量准则下的最优复制，然后运用一般的Clark公式与Malliavin分析得到了最优的套期保值策略．     

Strong Law of Large Numbers for Weighted Sums of Random Variables and Its Applications in EV Regression Models

This paper mainly studies the strong convergence properties for weighted sums of extended negatively dependent(END, for short) random variables. Some sufficient conditions to prove the strong law of large numbers for weighted sums of END random variables are provided. In particular, the authors obtain the weighted version of Kolmogorov type strong law of large numbers for END random variables as a product. The results that the authors obtained generalize the corresponding ones for independent ra...     

工程索赔决策支持系统的研究

工程索赔在工程管理中既重要又困难，它是经验型的工作。本文向索赔处理者提供了一个决策支持系统。本系统设计了结构化的索赔处理程序；建立了便于使用的储存着大量结构化案例的案例库；构造了含有多种计算公式和表格的模型库；设立了数据库，其中的数据可由其它系统的信息转换得到。     

随机巨灾索赔相依风险模型的动态最优再保险

在索赔风险时变、相依条件下,建立随机巨灾的可调态再保险模型.在指明超额赔款再保险为最优分保形式的基础上,讨论并发现目标函数随自留巨灾风险水平的增大,在任意相依结构下均先减后增的变化定理,从而获得了自留向量的一般性显式表达式.根据巨灾风险的特征,还在一类特定的相依结构下,以自留风险的期望效用和方差为优化目标,对自留向量进行了更为明确的表示并给出具体示例.结果表明,随着巨灾风险相依强度的上升,分保的满意度降低,经营稳定性减弱,对保险公司的负面影响很大.此时,为实现客观风险下的分保目标最优,常规风险的自留水平应随之增大,体现了动态再保险的优越性.     

The strong law of large numbers for pairwise NQD random variables

In this paper, the almost sure convergence for pairwise negatively quadrant dependent random variables is studied. The strong law of large numbers for pairwise negatively quadrant dependent random variables is obtained. Our results generalize and improve those on almost sure convergence theorems previously obtained by Marcinkiewicz (1937), Jamison (1965), Matula (1992) and Wu (2001) from the independent identically distributed (i.i.d.) case to pairwise NQD sequences.     

组合风险与单个资产风险间的定量关系——基于一致性风险测度的视角

在一致性风险测度研究的基础上,通过构建基于多因子模型的空间,从以往对一致性风险测度次可加的定性描述,转而研究组合风险与单个资产风险之间的定量关系,为一致性风险测度理论和风险分散化的深入研究提供新的视角.最后,在风险因子服从正态分布假设下,揭示了资产之间风险相互作用的一般机理,同时论证了M-V模型最优解也是任何均值-一致性风险测度模型的最优解.     

用二值响应模型检测银行贷款中的房地产抵押欺诈

银行贷款中的房地产抵押欺诈已经成为银行行业关心的主要问题。本文以某省商业银行分行包含诚实的和欺诈的借款抵押合同为研究样本,利用数据库数据,使用二值响应模型检测房地产抵押欺诈行为,并根据修正的、考虑错分类误差的Logit模型对用标准Logit模型未能检测出来的欺诈性抵押合同的比例进行估计,为更精确地识别房地产抵押欺诈提供新的认识工具并帮助抵押监控管理人员识别欺诈。     

Optimal Insurance-Package and Investment Problem for an Insurer

An insurance-package is a combination being tie-in at least two different categories of insurances with different underwriting-yield-rate. In this paper, the optimal insurance-package and investment problem is investigated by maximizing the insurer's exponential utility of terminal wealth to find the optimal combination-share and investment strategy. Using the methods of stochastic analysis and stochastic optimal control, the Hamilton-Jacobi-Bellman(HJB) equations are established, the optimal strategy and the value function are obtained in closed form. By comparing with classical results, it shows that the insurance-package can enhance the utility of terminal wealth, meanwhile,reduce the insurer's claim risk.     

我国商业车险奖惩系统的构建与评价

在商业车险定价中,通常根据保单的先验风险特征信息建立广义线性模型来厘定先验费率,然后根据保单的历史索赔信息应用奖惩系统对先验费率进行调整.本文基于一组商业车险保单2010-2015年的索赔次数数据,分别在泊松-伽马分布假设和负二项-贝塔分布假设下构建了奖惩系统,运用贝叶斯方法和极大似然法估计了模型参数,测算了奖惩系数,并与我国现行的奖惩系数进行了比较.实证研究结果表明,我国现行奖惩系统的设计结构比较单一,对保单经验索赔信息的使用不充分,且奖惩幅度过于温和.本文构建的奖惩系统充分利用了保单的先验风险特征信息与历史索赔信息,有效避免了对保单的重复性奖励和惩罚,提高了费率厘定结果的准确性和合理性.     

保险公司破产模型的进一步研究

引入一个新的概念——标准索赔额，建立一种新的破产模型并给出它的破产概率，从而使得破产概率更具有现实意义，并可作为衡量保险公司金融风险的一个重要指标。     

索赔到达间隔为几何分布风险模型的破产问题

讨论了索赔到达间隔时间服从几何分布,索赔额分布为一般离散型分布的一类连续时间风险模型的破产问题,先将风险模型纳入PDMP框架,借助于带离散分量的广义生成元的概念得到相关鞅,再利用测度变换理论得到破产概率的一般表达式,有趣的是破产函数不是连续的,而是逐段常值的.     

Optimal investment and proportional reinsurance in the Sparre Andersen model

From the insurer’s point of view,this paper studies the optimal investment and proportional reinsurance in the Sparre Andersen model.Under the criterion of maximizing the adjustment coefficient, the authors obtain the closed form expressions of the optimal strategy and the maximal adjustment coefficient,and derive the explicit expression of the ruin probability or its lower bound when the claim sizes are exponentially distributed.Some numerical examples are presented,which show the impact of model parameters on the optimal values.It can also be seen that the optimal strategy to maximize the adjustment coefficient is sometimes equivalent to those which minimize the ruin probability.