分层广义线性模型在准备金评估中的建模研究

考虑到赔付流量三角形数据同一事故年反复观测的纵向特征以及数据结构的层次性,建立了分层广义线性模型.与通常的随机模型相比,分层广义线性模型不但可以选择条件反应变量的分布而且风险参数分布范围也更加广泛.利用h-似然函数估计分层广义线性模型的模型参数,降低了计算量.为使模型具有可比性,评估模型的预测精度,推导了模型预测误差的估计式.为充分利用已知赔付信息,将赔付额和赔付次数两种赔付信息纳入未决赔款准备金评估模型,建立了两阶段分层广义线性模型.在线性预测量中考虑了各种固定效应和随机效应以及模型结构的散布参数,改进了线性预估量结构.研究表明:分层广义线性模型对于数据的各种分布及形式都具有很好的适应性,更加符合保险实务现实的赔付规律.     

Extensions of the Ho and Lee interest-rate model to the multinomial case

The paper presents a state dependent multinomial model of intertemporal changes in the term structure of interest rates. The model is a one-factor interest-rate model within the Markov family models for short-term interest rate and it extends the Ho and Lee [J. Finance XLI (5) (1986) 1001] binomial model. We derive the theoretical basis of the multinomial model, suggest a computational framework to evaluate the model's parameters and investigate the suitability of the model for the Italian market.     

Extension of the Arruda-Boyce model to the modelling of the curing process of polymers

A phenomenologically motivated finite strain general framework to simulate the curing of polymer have been developed and discussed in our recently published papers [2,4]. The Arruda-Boyce model is a classical hyperelastic model for polymeric materials. This contribution presents an extension of the Arruda-Boyce model towards modelling the curing process of polymers following our previous framework. In this paper, we will show how to model the elastic behaviour and shrinkage effects of the polymer curing process in the isothermal case using the Arruda-Boyce model. Several numerical examples have been demonstrated to verify our newly proposed modified approach in case of curing process. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A statistical model of the controller functions of the human temperature- regulating system in water

In a previous paper, a least-squares approach was used to develop a model of the control system's response to temperature stresses in an air environment. This procedure has now been applied to the case of temperature stresses during water immersion. The model presented here includes equations for predicting metabolic heat production and surface blood flow. In addition, upper and lower limits have been determined for each controller response. Validity of the model has been tested via simulation. The control system model developed in this study was incorporated in an existing complete temperature-regulation system simulation model. Thus modified, the complete model was used to simulate a number of published experiments. Graphical and statistical analysis indicates that the model is valid over a wide range of temperatures.     

Application of the Arlequin method in the virtual engineering design process

The creation of a holistic model which is able to represent the global dynamic behavior as well as local effects in certain regions leads to finite element models consisting of domains with different local meshes and a combination of different model dimensions. The different model domains have to be coupled such causing in an additional coupling error. The Arlequin method seems to be a flexible tool which has some advantages in comparison to alternative methods. In this paper the application of the Arlequin method on the coupling of a 3D continua model and a beam model is studied. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the quality of the data envelopment analysis model

The user of data envelopment analysis (DEA) has little available guidance on model quality. The technique offers none of the misspecification tests or goodness of fit statistics developed for parametric statistical methods. Yet, if a DEA model is to guide managerial policy, the quality of the model is of crucial importance. This paper suggests four alternative purposes of DEA modelling, and offers four measures of the quality of a DEA model which reflect those purposes. Using Monte Carlo simulation methods, it explores the performance of DEA under a wide variety of assumptions. It notes that four issues will have an important influence on model results: the distribution of true efficiencies in the study sample; the size of the sample; the number of inputs and outputs included in the analysis; and the degree of correlation between inputs and outputs. The paper concludes that any judgement about the reliability of model results must be dependent on the objective of the analysis.     

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。     

Exact Analysis of the State-Dependent Polling Model

We consider a polling model in which a number of queues are served, in cyclic order, by a single server. Each queue has its own distinct Poisson arrival stream, service time, and switchover time (the server's travel time from that queue to the next) distribution. A setup time is incurred if the polled queue has one or more customers present. This is the polling model with State-Dependent service (the SD model). The SD model is inherently complex; hence, it has often been approximated by the much simpler model with State-Independent service (the SI model) in which the server always sets up for a service at the polled queue, regardless of whether it has customers or not. We provide an exact analysis of the SD model and obtain the probability generating function of the joint queue length distribution at a polling epoch, from which the moments of the waiting times at the various queues are obtained. A number of numerical examples are presented, to reveal conditions under which the SD model could perform worse than the corresponding SI model or, alternately, conditions under which the SD model performs better than a corresponding model in which all setup times are zero. We also present expressions for a variant of the SD model, namely, the SD model with a patient server.     

On the weighting of the mean-absolute-deviation cost minimization model

The mean-absolute-deviation cost minimization model, which aims to minimize sum of the mean value and the absolute deviation (AD) of the total cost multiplied by a given non-negative weighting, is one of a number of typical robust optimization models. This paper first uses a straightforward example to show that the solution obtained by this model with some weightings is not actually an optimal decision. This example also illustrates that the mean-absolute-deviation cost minimization model cannot be regarded as the conventional weighted transformation of the relevant multiobjective minimization model aiming to simultaneously minimize the mean value and AD. This paper further proves that the optimal solution obtained by the mean-absolute-deviation cost minimization model with the weighting not exceeding 0.5 will not be absolutely dominated by any other solution. This tight upper bound provides a useful guideline for practical applications.     

On infinity of the discrete spectrum of operators in the Friedrichs model

The discrete spectrumof selfadjoint operators in the Friedrichs model is studied. Necessary and sufficient conditions of existence of infinitely many eigenvalues in the Friedrichs model are presented. A discrete spectrum of a model three-particle discrete Schrödinger operator is described.     

On some generalization of the DEA models

Inadequate results may arise in some instances of DEA model applications. For example, a data envelopment analysis (DEA) model may show ‘a notoriously inefficient unit’ as an efficient one. In addition, too many efficient units may appear in some DEA models. An elegant and subtle approach was proposed to deal with these problems, which is based on incorporating domination cones in DEA models. Yu, Wei and Brockett suggested the generalized DEA (GDEA) model that unifies and extends most of the well-known DEA models based on using domination cones. In this paper, we propose a model that is more general than the GDEA model, on the one hand, as it covers situations that the GDEA model cannot describe. On the other hand, our model enables one to construct step-by-step any model from the family of the GDEA models by incorporating artificial units and rays in the space of inputs and outputs in the Banker, Charnes, Cooper (BCC) model, which makes the process of model construction visible and more understandable. Moreover, we show that any GDEA model can be approximated by some BCC model.     

中国股票市场风险的实证分析研究

本文从实证角度说明了上证指数和深证成份指数存在着GARCH现象 ,并建立了沪、深两市股指波动率的IGARCH(1,1) M模型与EGARCH(1,1) M模型。将估计的IGARCH(1,1) M模型与EGARCH(1,1) M模型比较得出 ,对上证指数的波动率 ,IGARCH(1,1) M模型与EGARCH(1,1) M模型的模拟效果基本相同 ,而对深证成份指数的波动率 ,IGARCH M模型要略优于EGARCH M模型。同时还对两市的股指收益的波动率进行了预测分析     

On the global asymptotic stability of the equilibrium of the Lotka-Volterra equations in a varying environment

We consider a mathematical model describing the evolution of prey and predator populations in a varying environment. The model is a system of ordinary differential equations with a unique nontrivial equilibrium. We derive sufficient conditions for the global asymptotic stability of the equilibrium.     

On the use of the predictive likelihood of a Gaussian model

The predictive likelihood of a model specified by data is defined when the model satisfies certain conditions. It reduces to the conventional definition when the model is specified independently of the data. The definition is applied to some Gaussian models and a method of handling the improper uniform prior distributions is obtained for the Bayesian modeling of a multi-model situation where the submodels may have different numbers of parameters. The practical utility of the method is checked by a Monte Carlo experiment of some quasi-Bayesian procedures realized by using the predictive likelihoods. The Institute of Statistical Mathematics     

Optimization of the chemotherapy process on the base of the maximum principle

We consider an optimal control problems for the chemotherapy process on the base of a known dynamical model. The solution technique is connected with a combination of control modes determined in accordance with the Pontryagin maximum principle. We propose extremal control procedures with particular components supplementing the known therapy strategies within the considered model.     

染病者有常数输入的传染病模型

讨论在隔离措施下易感者和染病者都有常数移民的传染病模型.给出了模型的地方病平衡点,证明了地方病平衡点的稳定性.     

金融市场波动性CARR类模型与GARCH类模型的比较研究

在CARR模型基础上提出它的衍生模型ABSCARR模型,并利用广义误差分布(GED)讨论了它们的条件残差分布问题,最后运用CARR类模型对高频金融时间序列进行了实证分析.研究结果表明:CARR及其衍生模型在高频金融时间序列的价格波动性捕捉方面具有良好的效果,而GED的引入可以很好的用于分析CARR模型具体的条件分布情况,而CARR模型的条件残差分布应该并非只有指数分布与威布尔分布两种形式.     

引入特征AHP的PDEA评价模型研究

提出了基于特征AHP的带偏好DEA评价模型,该模型充分利用了带偏好约束锥的DEA方法能反映决策者对各准则的偏好程度,具备研究多个同类样本的"相对优劣性"评价的优势,并可有效地避免了由于引入偏好带来的主观性.最后,通过模型仿真、分析,验证了提出的评价模型的优点.     

On the Stationary Version of the Generalized Hyperbolic ARCH Model

This paper finds conditions under which the generalized hyperbolic ARCH-type model is strictly stationary. Properties of the model are investigated and in particular an estimation procedure is proposed. The resulting stationary model provides with a robust non-Gaussian ARCH-type alternative.