Multi-stage nested classification credibility quantile regression model

In insurance (or in finance) practice, in a regression setting, there are cases where the error distribution is not normal and other cases where the set of data is contaminated due to outlier events. In such cases the classical credibility regression models lead to an unsatisfactory behavior of credibility estimators, and it is more appropriate to use quantile regression instead of the ordinary least squares estimation. However, these quantile credibility models cannot perform effectively when the set of data has nested (hierarchical) structure. This paper develops credibility models for regression quantiles with nested classification as an alternative to Norberg’s (1986) approach of random coefficient regression model with multi-stage nested classification. This paper illustrates two types of applications, one with insurance data and one with Fama/French financial data.     

Optimal production inventory policy for defective items with fuzzy time period

In this paper, an optimal production inventory model with fuzzy time period and fuzzy inventory costs for defective items is formulated and solved under fuzzy space constraint. Here, the rate of production is assumed to be a function of time and considered as a control variable. Also the demand is linearly stock dependent. The defective rate is taken as random, the inventory holding cost and production cost are imprecise. The fuzzy parameters are converted to crisp ones using credibility measure theory. The different items have the different imprecise time periods and the minimization of cost for each item leads to a multi-objective optimization problem. The model is under the single management house and desired inventory level and product cost for each item are prescribed. The multi-objective problem is reduced to a single objective problem using Global Criteria Method (GCM) and solved with the help of Fuzzy Riemann Integral (FRI) method, Kuhn–Tucker condition and Generalised Reduced Gradient (GRG) technique. In optimum results including production functions and corresponding optimum costs for the different models are obtained and then are presented in tabular forms.     

模糊需求下的供应链收益共享契约模型

在模糊需求环境下,研究由单一供应商和零售商组成的两级供应链系统的协调机制问题。将市场需求视为模糊变量,建立不确定理论下,基于可信性分布的集成供应链模型和收益共享契约模型,并给出了模型中的最优策略。最后,以三角形模糊变量为例,通过数值算例对模型中的参数进行了求解,并分析批发价格和收益系数对其他参数的影响。研究结果表明,零售商的最优订购量在模糊需求中心点的左、右浮动,并随着零售价格的提高而增加;不同的收益系数对应不同的批发价格策略;通过改变收益系数可以实现供应链成员之间的完美协调。     

Logistics distribution centers location problem and algorithm under fuzzy environment

Distribution centers location problem is concerned with how to select distribution centers from the potential set so that the total relevant cost is minimized. This paper mainly investigates this problem under fuzzy environment. Consequentially, chance-constrained programming model for the problem is designed and some properties of the model are investigated. Tabu search algorithm, genetic algorithm and fuzzy simulation algorithm are integrated to seek the approximate best solution of the model. A numerical example is also given to show the application of the algorithm.     

卤水监测数据的合理性检验

介绍了卤水试验监测数据的合理性的几种检验方法,以保证实验室监测数据的准确性与可靠性.     

Estimation of IBNR claims by credibility theory

We develop a stochastic multiplicative model for the forecasting of IBNR claims. The factor depending on the accident year is credibility adjusted.The title of this note also suits for the papers by Straub (1971) and Kramreiter and Straub (1973). We made stronger assumptions simplifying drastically the numerical calculations and the parameter estimation problem.As showed in the numerical illustrations, the developed method is also applicable in case of scarce irregular data.     

Non-linear regression in credibility theory

Let X be a random vector with distribution depending on a parameter treated as a random variable ?. The usual linear regression assumption is that E(X|?) can be displayed in the form yβ(?) where y is a fixed design matrix and β(?) an unknown vector. In the present paper we assume that E(X|?) is a rather arbitrary function ?(β(?)) of the unknown vector β(?) and we derive credibility approximations for β(?).     

A characterization of the class of credibility matrices corresponding to a certain class of discrete distributions

Recently (see De Vylder & Goovaerts (1984), this issue) so called credibility matrices have been introduced and studied in the framework of general properties of matrices, such as non-negativity, total positivity etc. In the present note we characterize a class of credibility matrices generated by the normed sequence of functions (p_l, p_l,…, p_n) on K = [0, b] where $\text{p}{}_{\mathrm{i}}\text{(θ) =?(i)g(θ)h}{}^{\mathrm{i}}\text{(θ)}$, i=0, …, n, θ ? K, and where ?, g, h are nonnegative (eventually depending on n, n may be finite or infinite). For simplicity we suppose h to be monotonic and continuous.     

A production–recycling–inventory system with imprecise holding costs

This paper presents an optimal control recycling production inventory system in fuzzy environment. The used items are bought back and then either put on recycling or disposal. Recycled products can be used for the new products which are sold again. Here, the rate of production, recycling and disposal are assumed to be function of time and considered as control variables. The demand inversely depends on the selling price. Again selling price is serviceable stock dependent. The holding costs (for serviceable and non-serviceable items) are fuzzy variables. At first we define the expected values of fuzzy variable, then the system is transferred to the fuzzy expected value model. In this paper, an optimal control approach is proposed to optimize the production, recycling and disposal strategy with respect so that expected value of total profit is maximum. The optimum results are presented both in tabular form and graphically.     

两阶段模糊运输期望值模型及其逼近方法

基于可信性理论和两阶段模糊优化方法,提出一类带有模糊参数的两阶段运输期望值模型.由于提出运输问题包含带有无限支撑的模糊变量系数,因此它是一个无限堆的优化问题.然后,讨论两阶段模糊运输期望值问题的逼近方法并且将逼近方法嵌套到遗传算法中产生一个基于遗传算法的逼近方法求解提出的两阶段模糊运输期望值问题.最后,给出一个数值例子...