非寿险业务未决赔款准备金的两阶段广义线性模型估计

本文以非寿险业务未决赔款准备金估计的确定性方法-PPCI法的思想为基础,分两阶段建立广义线性模型,分别对索赔次数和已发生每案赔付额进行估计,进而得到未决赔款准备金的估计值,并对模型的预测误差进行估计。文中通过一个实例对所述方法进行验证,并从预测误差的角度与其它模型进行比较。最后对该模型特点进行了总结。     

基于同单调理论的IBNR准备金估计的随机界

在对IBNR准备金估计的随机模型存在的不足进行分析的基础上,对采用二阶段广义线性模型得到的各单元IBNR准备金估计和的分布问题进行讨论.在考虑折现因子的基础上,采用同单调理论,得到各单元准备金估计的和在凸序意义下的随机界,并通过一个实例对所述方法进行验证.     

Hoerl曲线的改进及其在非寿险未决赔款准备金估计中的应用

对基于Hoerl曲线的非寿险未决赔款准备金估计模型的不足进行了讨论,并对其进行了改进.将改进的Hoerl曲线做为预测量而建立的指数族非线性模型具有更大的灵活性,因而更适用于未决赔款准备金的估计.通过模拟实验对改进的Hoerl曲线在未决赔款准备金估计中的应用进行了验证,并与经典泊松链梯模型以及基于Hoerl曲线的模型进行了对比分析.结论表明,对于先缓慢增长至顶点,然后快速回落的赔付模式,改进的Hoerl曲线具有更好的预测效果.     

基于有限服务排队系统的未决赔款准备金分布

若保险赔付工作中赔付人员有限,根据服务人员有限的排队系统的性质,可以研究保险公司所需计提的未决赔款准备金的分布函数.当假设赔付服务工作人员为c个,使用M/M/c/∞和G/M/c/∞排队系统的性质可以得到未决赔款准备金分布函数和年末所需增加计提的未决赔款准备金的分布及其界值.当假设赔付服务工作人员仅一个,使用M/G/1/∞排队系统的性质可以得到此时未决赔款准备金的分布函数.并且在假设损失赔付额取正整数的条件下,得到年末保险公司所需增加计提的未决赔款准备金分布的递推公式.而且通过计算实例表明结论的实用性,及所得到的递推公式在以往难以准确求解未决赔款准备金分布时是十分有效的.     

广义加权损失函数下未决赔款准备金的信度估计

为了使得估计的准备金不依赖于先验分布的具体形式,在贝叶斯链梯模型中,采用信度理论的思想,在广义加权损失函数下得到链梯因子的信度估计,建立了案均赔款法下的未决赔款准备金模型.最后,给出保险公司的实际例子,将得到的信度估计与经典链梯法和随机链梯法估计进行了比较.结论显示,方法对未决赔款准备金是有效的.     

线性模型中误差方差估计的随机加权逼近

本文利用对样本随机加权的思想,构造了线性模型中误差方差估计的抽样分布的一种新的逼近,与传统的Boostrop方法相比,随机加权逼近不需要样本独立同分布的假设,在很广泛的条件下,我们证明了新逼近方法的相合性。     

广义加权损失函数下准备金的分位信度估计

由于聚合数据是个体数据的加总,会失去一些有用信息.针对个体数据模型,分位回归模型可以直接求取未决赔款准备金的分位数,并且对数据中存在的异常值的敏感度不高.在程纪(2020)模型基础上,将分位回归模型与信度理论相结合,将多个流量三角形的增量赔款数据看成是相同日历年下的重复性多次观测,体现样本数据的分层结构,克服经典信度模型中只有一条回归线的弊端,在广义加权损失函数下得到准备金的信度估计,并给出参数估计.     

线性模型中M估计分布的随机加权方法逼近

在线性模型中,M估计的渐近分布通常都涉及到不易估计的未知误差分布的某些量,如果要估计渐近方差,就需对这些冗余参数进行估计.利用随机加权方法可以避免先对误差分布中的冗余参数进行估计.给出了当自变量是随机变量时,M估计分布的随机加权逼近,证明了M估计分布的随机加权逼近是一致相合的.当取不同的凸函数,样本大小和随机权时,进一步利用蒙特卡洛方法研究估计分布.研究表明随机权取泊松权时,不仅达到同样的效果而且可以减小计算量.     

半参数回归模型中小波估计的随机加权逼近速度

把小波光滑方法和随机加权方法结合在一起，获得了半参数回归模型中参数分量的小波估计的随机加权逼近速度为σ(n^-1/2)。因此，从大样本意义上说，小波光滑方法和随机加权方法对半参数回归模型是可用的。     

两个多面体之交上的最佳逼近与保凸回归问题

本文提出了一种求Hilbert空间中给定点x0在两个多面体K’与K”之交上的最佳逼近的算法，它把问题化归为有限次求点在K’与K”中的最佳逼近的问题．由于保凸回归问题可表述为求某点x0在两个锐锥之交上的最佳逼近问题，故结合熟知的锐锥逼近的PAVA算法即可得到保凸回归的有限算法．文章还计算了一个保凸回归问题的实例．     

Approximation for Semilinear Stochastic Evolution Equations

We investigate the approximation by space and time discretization of quasi linear evolution equations driven by nuclear or space time white noise. An error bound for the implicit Euler, the explicit Euler, and the Crank–Nicholson scheme is given and the stability of the schemes are considered. Lastly we give some examples of different space approximation, i.e., we consider approximation by eigenfunction, finite differences and wavelets.     

Term Structure Models in Multistage Stochastic Programming: Estimation and Approximation

This paper investigates some common interest rate models for scenario generation in financial applications of stochastic optimization. We discuss conditions for the underlying distributions of state variables which preserve convexity of value functions in a multistage stochastic program. One- and multi-factor term structure models are estimated based on historical data for the Swiss Franc. An analysis of the dynamic behavior of interest rates generated with these models reveals several deficiencies which have an impact on the performance of investment policies derived from the stochastic program. While barycentric approximation is used here for the generation of scenario trees, these insights may be generalized to other discretization techniques as well.     

未决赔款准备金评估的随机性Munich链梯法

精算实务界通常采用链梯法等确定性方法评估未决赔款准备金,这些评估方法存在一定缺陷,一方面不能有效考虑保险公司历史数据中所包含的已决赔款和已报案赔款数据信息,另一方面只能得到未决赔款准备金的均值估计,不能度量不确定性。为了克服这些缺陷,本文结合Mack模型假设和非参数Bootstrap重抽样方法,提出了未决赔款准备金评估的随机性Munich链梯法,并应用R软件对精算实务中的实例给出了数值分析。     

Meshfree Approximation for Stochastic Optimal Control Problems

In this work,we study the gradient projection method for solving a class of stochastic control problems by using a mesh free approximation ap-proach to implement spatial dimension approximation.Our main contribu-tion is to extend the existing gradient projection method to moderate high-dimensional space.The moving least square method and the general radial basis function interpolation method are introduced as showcase methods to demonstrate our computational framework,and rigorous numerical analysis is provided to prove the convergence of our meshfree approximation approach.We also present several numerical experiments to validate the theoretical re-sults of our approach and demonstrate the performance meshfree approxima-tion in solving stochastic optimal control problems.     

A Strong Approximation Theorem for Stochastic Recursive Algorithms

The constant stepsize analog of Gelfand–Mitter type discrete-time stochastic recursive algorithms is shown to track an associated stochastic differential equation in the strong sense, i.e., with respect to an appropriate divergence measure.     

Stochastic Ordering of Multivariate Normal Distributions

We show an interesting identity for Ef(Y) – Ef(X), where X, Yare normally distributed random vectors and f is a function fulfilling some weak regularity condition. This identity will be used for a unified derivation of sufficient conditions for stochastic ordering results of multivariate normal distributions, some well known ones as well as some new ones. Moreover, we will show that many of these conditions are also necessary. As examples we will consider the usual stochastic order, convex order, upper orthant order, supermodular order and directionally convex order.     

Convex upper and lower bounds for present value functions

In this paper we present an efficient methodology for approximating the distribution function of the net present value of a series of cash‐flows, when discounting is presented by a stochastic differential equation as in the Vasicek model and in the Ho–Lee model. Upper and lower bounds in convexity order are obtained. The high accuracy of the method is illustrated for cash‐flows for which no analytical results are available. Copyright © 2001 John Wiley & Sons, Ltd.     

广义双随机矩阵反问题及其应用

研究广义双随机矩阵反问题.给出广义双随机矩阵的最小二乘解,得到了解的具体表达形式.并讨论了用广义双随机矩阵构造给定矩阵的最佳逼近问题,给出该问题有解的充分必要条件和解的表达形式.包括算法及数值例子.