个体风险模型的Poisson复合模型近似

本文在近乎最一般的假定下，简述了个体风险模型的Poisson复合模型近似．特别地，借助风险间停止损失保费的总差异给出了这一近似的精度．     

保险风险模型的序关系及其误差

从停止损失序的角度,探讨了用集体风险模型来近似个体风险模型时,随机风险理赔总额S的一般情况,我们推广现有文献(如Goovaerfs)的关于单因模型的结果,得到了各模型间S的序的关系(定理1),并给出了各模型S之间的误差公式(定理3).     

某些保险风险序的性质及其相互关系

本文讨论了几种保险风险次序的性质及它们之间的相互关系 ,利用停止损失限额变换的特性讨论了停止损失收敛的性质和在极限状态下风险次序的传递闭包的性质 ,得到了停止损失收敛的一种等价表示 ,并对两种具体风险序的传递闭包给出了等价的风险序表示 .     

多周期多目标条件风险值模型

在商业、工业、电力和房地产等行业中存在许多复杂的多周期风险决策问题,它的数学模型研究对于解决这些问题具有重要的作用.作者建立了一种新的多周期多目标条件风险值(CVaR)数学模型理论和方法.先定义了一种带时间段的多周期多目标损失函数下的α-VaR和α-CVaR值,给出了一类多周期多目标CVaR最优化模型.然后,证明了多目标意义下的对应模型的等价定理,给出了多周期多目标CVaR模型的近似求解等价模型.最后,建立了一种生产企业在供过于求和供不应求两种情形下产生的多周期双目标CVaR模型,针对一个电力生产企业进行的数值实验,表明了模型可以得到在最小供给的用电损失分布下的各周期下的相匹配供电策略,可以帮助供电部门各个时期供电不平衡状况下的风险控制.     

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.     

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.     

商业银行操作风险的Buhlmann估计模型

对银行操作风险产生的各类损失量,关于操作风险水平条件独立情况,建立一种新的银行操作风险损失额的Buhlmann估计模型。并对模型进行了实证分析。     

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.     

CVaR风险度量模型在投资组合中的运用

风险价值(VaR)是近年来金融机构广泛运用的风险度量指标，条件风险价值(CVaR)是VaR的修正模型，也称为平均超额损失或尾部VaR，它比VaR具有更好的性质。在本中，我们将运用风险度量指标VaR和CVaR，提出一个新的最优投资组合模型。介绍了模型的算法，而且利用我国的股票市场进行了实证分析，验证了新模型的有效性，为制定合理的投资组合提供了一种新思路。     

相依回归模型的参数估计的风险估计

本文给出了相依回归模型的ＯＬＳ估计，ＧＬＳ估计和ＲＧＬＳ估计在二次损失和Ｆｉｓｈｅｒ损失下的风险估计不等式。     

A Quasilinear Hierarchical Size-Structured Model: Well-Posedness and Approximation

A finite difference approximation to a hierarchical size-structured model with nonlinear growth, mortality and reproduction rates is developed. Existence-uniqueness of the weak solution to the model is established and convergence of the finite-difference approximation is proved. Simulations indicate that the monotonicity assumption on the growth rate is crucial for the global existence of weak solutions. Numerical results testing the efficiency of this method in approximating the long-time behavior of the model are presented.     

The robustness of the semi-Markov and delay time single-component inspection models to the Markov assumption

The context of planned preventive maintenance lends itself readilyto probabilistic modelling. Indeed, many of the published theoreticalmodels to be found in the literature adopt a Markov approach,where states are usually ‘operating’, ‘operatingat one of several levels of deterioration’, and ‘failed’.However, most of these models assume the required Markovianproperty and do not address the issue of testing the assumption,or the related task of estimating parameters. It is possiblethat data are inadequate to test the assumption, or that theMarkov property is believed to be not strictly valid, but acceptableas an approximation. In this paper we consider within a specificinspection–maintenance context the robustness of a Markov-basedmodel when the Markov assumption is not valid. This is achievedby comparing the output of an exact delay time model of an inspection–maintenanceproblem with that of a semi-Markov approximation. The importanceof establishing the vadility of the Markov property in the modellingapplication is highlighted. If the plant behaviour is seen tobe nearly Markov, in the case considered the semi-Markov modelgives a good approximation to the exact model. Conversley ifthe Markov assumption is not a good approximation, the semi-Markovmodel can lead to inappropriate advice.     

Protein folding in the HP model on grid lattices with diagonals

The protein folding problem, i.e., the computational prediction of the three-dimensional structure of a protein from its amino acid sequence, is one of the most important and challenging problems in computational biology. Since a complete simulation of the folding process of a protein is far too complex to handle, one tries to find an approximate solution by using a simplified, abstract model. One of the most popular models is the so-called HP model, where the hydrophobic interactions between the amino acids are considered to be the main force in the folding process, and furthermore the folding space is modeled by a two- or three-dimensional grid lattice.In this paper, we will present some approximation algorithms for the protein folding problem in the HP model on an extended grid lattice with plane diagonals. The choice of this kind of lattice removes one of the major drawbacks of the original HP model, namely the bipartiteness of the grid which severely restricts the set of possible foldings. Our algorithms achieve an approximation ratio of for the two-dimensional and of for the three-dimensional lattice. This improves significantly over the best previously known approximation ratios for the protein folding problem in the HP model on any lattice.     

基于最小二乘近似的模型平均方法

本文提出基于最小二乘近似的模型平均方法.该方法可用于线性模型、广义线性模型和分位数回归等各种常用模型.特别地,经典的Mallows模型平均方法是该方法的特例.现存的模型平均文献中,渐近分布的证明一般需要局部误设定假设,所得的极限分布的形式也比较复杂.本文将在不使用局部误设定假设的情形下证明该方法的渐近正态性.另外,本文将该方法发展到维数发散的情形.数值结果显示了该方法的优势.     

Extension of Some Classical Results on Ruin Probability to Delayed Renewal Model

Embrechts and Veraverbeke investigated the renewal risk model and gave a tail equivalence relationship of the ruin probabilities (?)(x) under the assumption that the claim size is heavy-tailed, which is regarded as a classical result in the context of extremal value theory. In this note we extend this result to the delayed renewal risk model.     

Numerical three-dimensional free surface circulation model for the South Biscayne Bay,Florida

A three– dimensional, time dependent free surface model has been developed for predicting circulation and surface height variations in a tidal bay. An explicit finite difference numerical solution is obtained by transforming the vertical coordinate in the governing model equations. The transformed geometry consists of a fixed, flat free surface and a constant depth basin for easy computation. The ocean–bay interface open boundary condition is incorporated into this hydrodynamic model without approximation, and yields rather accurate results for the bay circulation and tide level variations. The numerical method employs a staggered grid Richardson lattice, which has the inherent property of not requiring calculation of the tangential velocity components on solid surfaces. The momentum equations ignore horizontal diffusion which is small for the South Biscayne Bay, for which vertical diffusion and advection dominate.     

更新风险模型和延迟更新风险模型中破产概率的若干结果

本文进一步研究更新风险模型和延迟更新风险模型中的破产概率ψ(χ),这里χ是保险公司的初始资本.在假定个体索赔分布是重尾的前提下,得到了与经典模型相一致的破产概率ψ(χ)的一个尾等价关系.     

Multi-population mortality models: A factor copula approach

Modeling mortality co-movements for multiple populations have significant implications for mortality/longevity risk management. A few two-population mortality models have been proposed to date. They are typically based on the assumption that the forecasted mortality experiences of two or more related populations converge in the long run. This assumption might be justified by the long-term mortality co-integration and thus be applicable to longevity risk modeling. However, it seems too strong to model the short-term mortality dependence. In this paper, we propose a two-stage procedure based on the time series analysis and a factor copula approach to model mortality dependence for multiple populations. In the first stage, we filter the mortality dynamics of each population using an ARMA–GARCH process with heavy-tailed innovations. In the second stage, we model the residual risk using a one-factor copula model that is widely applicable to high dimension data and very flexible in terms of model specification. We then illustrate how to use our mortality model and the maximum entropy approach for mortality risk pricing and hedging. Our model generates par spreads that are very close to the actual spreads of the Vita III mortality bond. We also propose a longevity trend bond and demonstrate how to use this bond to hedge residual longevity risk of an insurer with both annuity and life books of business.     

A Class of Ruin Probability Mo del with Dep endent Structure

In this paper, we study a class of ruin problems, in which premiums and claims are dependent. Under the assumption that premium income is a stochastic process, we raise the model that premiums and claims are dependent, give its numerical characteristics and the ruin probability of the individual risk model in the surplus process. In addition, we promote the number of insurance policies to a Poisson process with parameter λ, using martingale methods to obtain the upper bound of the ultimate ruin probability.