成比例附加故障混合模型

Frailty模型和可加故障模型在研究各种风险因素与疾病发生原因的关系中提供了两种重要的方法.在不知哪个模型更适合数据时,涵盖这两个模型的成比例附加故障模型提供了一个备选模型.Frailty基本上是观察不到的,需要考虑对应的混合模型.本文研究了成比例附加故障混合模型的年龄性质、相依性质.并对该模型中的那些随机变量进行了随机比较.     

经济增长的随机AK模型

本文以经济增长AK模型(模型Ⅰ)作为基本模型,将人口数量作为不确定性的来源,建立了经济增长的随机AK模型(模型Ⅱ).分析了模型Ⅱ解的存在唯一性和M arkov性,探讨了模型Ⅱ的零均衡解的稳定性及资本-劳动比率的动态性质.     

北京市水资源利用建模分析研究

以北京市为例,分别应用无偏灰色GM(1,1)模型和非线性模型对北京市2001年-2010年的用水量进行了建模,利用最优化方法,计算了上述两种模型的最优组合模型,通过三种模型分别计算了北京市2001年-2010年的水资源利用量,并与北京市2001年-2010年的实际用水量进行了对比,采用精度检验方法,分别对无偏灰色模型,非线性模型和组合模型进行了精度检验,计算结果表明,加权组合模型是三种模型中精度最高的模型,通过组合模型计算得出的用水量值与实际水资源利用量相比误差最小,由此得出,可以利用组合模型对北京市未来的水资源利用量进行预测,预测结果可为其他相关研究提供参考.     

一类多指标对象评价模型

以C2R模型为基础给出了一类多指标对象评价模型——C2RM模型.我们首先定义了决策单元的优势集,论证了C2RM模型比一类多目标规划模型在优化意义上更进一步——排除了此类多目标规划模型的一些优势集为空的Pareto有效解.我们建立的C2RM模型是线性规划模型,易于判定一个决策单元是否DEA有效.在优势集性质基础上我们进一步定义了C2RM模型下DEA有效决策单元的实际有效率,并给出了所有决策单元的一种排序,最后举例予以说明.     

关于ARMA-BP神经网络组合模型的财政收入预测

本文研究了ARMA-BP神经网络组合模型预测的问题.利用最大最小贴近度评价方法,获得了ARMA-BP神经网络组合模型对应的贴近度差值大于单一模型的结果,推广了组合模型比单一模型预测精度更优的结果.     

人口迁移模型的改进及系统动力学仿真预测

求出了Keyfitz模型和Rogers模型的理论解,并以Rogers模型为例,对人口迁移模型进行了改进,使之适用范围更广.在人口迁移模型的基础上,建立了系统动力学模型,并对江西省的人口迁移问题进行了仿真预测,模拟出了江西省农村人口、城镇人口及城市化率的变化趋势.     

房地产行业的数学建模分析

分别建立了需求模型,供给模型,房地产与其他产业的关系模型,房价模型及房地产发展趋势的预测模型,并对影响模型的相应因素做了简要的分析.     

多图模型的联合估计的群桥方法

高斯图模型研究独立随机变量之间的关系.主要针对该模型,提出了一种分层惩罚连接单个图模型估计的多图模型.研究了新模型的高维统计性质,给出模型的参数估计,并得到了相合性及稀疏性两大理论.     

贝叶斯网络仿真元模型及其在装备战场损伤仿真中的应用研究

结合装备战场损伤仿真系统,研究了贝叶斯网络仿真元模型的构建方法.从条件概率角度描述了仿真模型输入参数与输出参数之间的映射关系,研究了构建贝叶斯网络仿真元模型的可行性,分析了贝叶斯网络仿真元模型的优点;研究了贝叶斯网络仿真元模型构建过程中的关键问题,包括:元模型参数的确定、原始模型参数向贝叶斯网络节点的转化、联结强度的计算、衍生元模型的构建;针对不完全信息条件下装备战场损伤快速定位问题,研究了基于K2算法的贝叶斯网络仿真元模型构建方法;构建了某型高炮的战场损伤贝叶斯网络仿真元模型.     

人民币汇率决定的资金流量分析建模

本文给出了人民币汇率决定模型，并对货币供需、资金流量进行了分析．该模型参照了Ｒｏｂｉｍｓｏｎ的国际贸易条件理论、Ａｌｅｘａｎｄｅｒ吸收理论、特别是Ｂａｒｒｏ—Ｃａｌｖｏ—Ｒｏｂｒｉｇｕｅｚ融资产组合平衡与货币分析法于一体的货币主义的货币替代模型．这个模型体系由三部分组成：基本模型、动态模型、调控模型．基于这三个模型，对汇率决定进行了一般的均衡分析、走势分析与调控分析．     

带有初始风险资产的风险投资决策模型

讨论了一类在投资时期初允许带有一部分初始风险资产的风险投资组合决策问题,给出了一个满足总体风险约束下以净收益最大化作为决策目标的资产投资组合的数学规划模型。并由该数学规划的性质,给出该类问题的一个简化的线性规划决策形式。     

非时齐复合Poisson风险模型的破产特征量分析

该文将经典风险模型推广到非时齐复合Poisson风险模型.首先,运用经典方法和时变方法,计算了该模型下的破产特征量,且得到了更新方程的解析表达式.其次,定义了时变后相应模型的一个广义的Gerber-Shiu函数,验证了时变方法对非时齐Poisson风险模型的有效性.最后,当单次索赔量服从指数分布时,计算了相应的破产概率和Gerber-Shiu函数.     

基于Copula的供应链金融质物组合价格风险测度研究

本文选取白银、铝和铜三种供应链金融质物作为研究对象,在分析三种质物收益率统计特征的基础上,引入Copula模型刻画供应链金融业务中质物收益率的“尖峰厚尾”特征以及质物收益率之间的非线性相关结构;采用Monte Carlo模拟方法测度考虑到极端情况下的质物组合价格风险值CVaR;利用时间平方根法则测度长周期视角下质物组合的价格风险。将CVaR与VaR测度结果进行对比,比较分析短期价格风险与长期价格风险,将Copula模型与传统风险测度方法下计算出的风险值进行对比,以期选取最优测度供应链金融质物组合长期价格风险模型。研究结果表明:从单一质物价格波动特征来看,三种单一质物的收益率均存在非正态分布和“尖峰厚尾”特征,具有一般金融资产收益率分布的特点。从模型的有效性来看,第一,CVaR比VaR能够更好地、全面地测度供应链金融质物组合的价格风险;第二,基于Copula模型的风险测度结果比传统集成风险测度结果的准确性高;第三,平方欧式距离法结果表明在五种Copula模型中,t-Copula是最优刻画供应链金融质物组合收益率间的相依关系的模型。从长短期风险测度结果来看,随着风险期限的增加,质物组合的价格风险值随之增大,以往研究中用短期风险测度往往会低估商业银行所面临的价格风险,不利于商业银行资金信贷的优化配置。得到的结论对我国商业银行开展供应链金融业务防范价格风险提供了量化支持。     

Moments of the Time of Ruin, Surplus Before Ruin and the Deficit at Ruin in the Erlang（N） Risk Process

In this paper we consider the ＂penalty＂ function in the Erlang（n） risk model. Using the integro- differential equation we established, we obtain the explicit expressions for the moments of Erlang（2） risk model. When the claim size distribution is Light-Tailed and the penalty function is bounded, we obtain the exact representations for the moments of Erlang（n） risk model.     

Joint distributions of some actuarial random vectors for the Cox risk model

The main purpose of this paper was to investigate the joint distributions of some actuarial vectors that contain the ruin time for the Cox risk model. Joint distributions of some actuarial vectors such as those containing the ruin time, the maximum surplus before ruin, duration of the surplus being negative, and others are important for measuring the risk management level and the severity caused by ruin. In the past decade, great literatures have devoted to the study of these distributions for classical models, such as the compound Poisson model and the perturbed compound Poisson model etc. The main result of this paper provides the joint distributions of these actuarial vectors for the Cox risk model—a model with wide applications in risk theory. The main method of this paper is to apply the idea of ‘operational time scale’ to the Cox model, which enables us to solve our problem by intergrading some existing results for the compound Poisson risk model. To some extent, we can view our work as an extension of joint distributions of some actuarial vectors for the compound Poisson risk model to the ones for the Cox risk model. Copyright © 2011 John Wiley & Sons, Ltd.     

Asymptotic aspects of the Gerber-Shiu function in the renewal risk model using Wiener-Hopf factorization and convolution equivalence

We study the asymptotic behavior of the Gerber-Shiu expected discounted penalty function in the renewal risk model. Under the assumption that the claim-size distribution has a convolution-equivalent density function, which allows both heavy-tailed and light-tailed cases, we establish some asymptotic formulas for the Gerber-Shiu function with a fairly general penalty function. These formulas become completely transparent in the compound Poisson risk model or for certain choices of the penalty function in the renewal risk model. A by-product of this work is an extension of the Wiener-Hopf factorization to include the times of ascending and descending ladders in the continuous-time renewal risk model.     

Local asymptotic behavior of the survival probability of the equilibrium renewal model with heavy tails

Recently, Tang established a local asymptotic relation for the ruin probability in the Cramer-Lundberg risk model. In this short note we extend the corresponding result to the equilibrium renewal risk model.     

The impact of the determinants of mortality on life insurance and annuities

Extended risk classification has become an important issue recently in life insurance and annuity markets. Various risk factors have been explored and identified by past research. Using those risk factors, one can construct various risk classes. This enables insurers to provide more equitable life insurance and annuity benefits for individuals in different risk classes and to manage mortality/longevity risk more efficiently. The challenge of modeling mortality using various risk factors is to reflect complicated mortality dynamics in a model while maintaining statistical significance. This paper discusses the development of a mortality model that reflects the impact of various risk factors on mortality. Longitudinal survey data from the Canadian National Population Health Survey was used to determine the significant risk factors and quantify their effect on mortality. The model is used to illustrate how the various risk factors influence actuarial present values of life insurance and annuity benefits.     

Analysis of the multiple roots of the Lundberg fundamental equation in the PH (n) risk model

In the study of the Sparre Andersen risk model with phase‐type (n) inter‐claim times (PH (n) risk model), the distinct roots of the Lundberg fundamental equation in the right half of the complex plane and the linear independence of the eigenvectors related to the Lundberg matrix L_δ(s) play important roles. In this paper, we study the case where the Lundberg fundamental equation has multiple roots or the corresponding eigenvectors are linearly dependent in the PH (n) risk model. We show that the multiple roots of the Lundberg fundamental equation det[L_δ(s)] = 0 can be approximated by the distinct roots of the generalized Lundberg equation introduced in this paper and that the linearly dependent eigenvectors can be approximated by the corresponding linearly independent ones as well. Using this result we derive the expressions for the Gerber–Shiu penalty function. Two special cases of the generalized Erlang(n) risk model and a Coxian(3) risk model are discussed in detail, which illustrate the applicability of main results. Finally, we consider the PH(2) risk model and conclude that the roots of the Lundberg fundamental equation in the right half of the complex plane are distinct and that the corresponding eigenvectors are linearly independent. Copyright © 2011 John Wiley & Sons, Ltd.     

古典风险模型的破产概率与M/G/1忙期的最大工作量的分布

本文考虑了古典风险模型与排队论中M/G/1模型关系, 利用古典风险模型的破产概率导出了M/G/1中一个忙期内最大工作量的分布.