不完全信息下三度价格歧视的有效性研究

基于不完全信息静态博弈模型,讨论了相互竞争的两厂商在双方都掌握的线性需求函数和一方随机选取的线性成本函数这样的不完全信息情况下实施三度价格歧视的有效性问题,且给出了双方实施三度价格歧视的最优产量,最优价格以及最大利润公式,并把相关结论与基于完全信息静态博弈的三度歧视定价和不完全信息静态博弈的统一定价进行对比,得出了许多重要的结论.     

Recursive methods for a multi-dimensional risk process with common shocks

In this paper, a multi-dimensional risk model with common shocks is studied. Using a simple probabilistic approach via observing the risk processes at claim instants, recursive integral formulas are developed for the survival probabilities as well as for a class of Gerber-Shiu expected discounted penalty functions that include the surplus levels at ruin. Under the assumption of exponential or mixed Erlang claims, the recursive integrals can be simplified to give recursive sums which are computationally more tractable. Numerical examples including an optimal capital allocation problem are also given towards the end.     

Adaptive surrogate-based design optimization with expected improvement used as infill criterion

A prominent advantage of using surrogate models in structural design optimization is that computational effort can be greatly reduced without significantly compromising model accuracy. The essential goal is to perform the design optimization with fewer evaluations of the typically finite element analysis and ensuring accuracy of the optimization results. An adaptive surrogate based design optimization framework is proposed, in which Latin hypercube sampling and Kriging are used to build surrogate models. Accuracy of the models is improved adaptively using an infill criterion called expected improvement (EI). It is the anticipated improvement that an interpolation point will lead to the current surrogate models. The point that will lead to the maximum EI is searched and used as infill points at each iteration. For constrained optimization problems, the surrogate of constraint is also utilized to form a constrained EI as the corresponding infill criterion. Computational trials on mathematical test functions and on a three-dimensional aircraft wing model are carried out to test the feasibility of this method. Compared with the traditional surrogate base design optimization and direct optimization methods, this method can find the optimum design with fewer evaluations of the original system model and maintain good accuracy.     

ON THE CRAM(E)R-LUNDBERG RISK MODEL WITH A CONSTANT FORCE OF INTEREST AND SURPLUS-DEPENDENT LOSS-CARRY-FORWARD TAX STRUCTURE

本文研究了带常数利率和盈余相依型loss-carry-forward税收系统的Cramér-Lundberg风险模型.利用无穷小分析方法及该过程具有的的强马氏性,得出了保险公司从开始运营到破产期间税收折现总额的数学期望表达式.作为例子,本文给出了指数分布索赔假定下该税收折现函数的具体表达式.     

The Monge Problem in Banach Spaces

In this paper, we generalize the Kantorovich functional to K?the-spaces for a cost or a profit function. We examine the convergence of probabilities with respect to this functional for some K?the-spaces. We study the Monge problem: Let be a K?the-space, P and Q two Borel probabilities defined on a Polish space M and a cost function . A K?the functional is defined by (P, Q) = inf where is the law of X. If c is a profit function, we note . (P, Q) = sup Under some conditions, we show the existence of a Monge function, φ, such that , or .      

基于线性规划博弈的供应链配送问题

着重建立了供应链配送问题的线性规划模型,分析说明了配送合作联盟对各成员是有利的.在配送博弈中,根据配送问题的对偶最优解和配送博弈核心之间的关系,构造了收益分配函数并证明了配送博弈的核心非空、所对应的分配方案稳定等性质.最后通过算例应用验证了模型和分配函数的有效性.     

三种不同需求分布条件下报童问题期望费用的计算

报童问题是运筹学中典型的随机性存贮模型.目前很多运筹学和管理科学教科书一般只给出报童问题最优订购量应该满足的条件,而没有给出具体的期望费用的表达式,这对于报童问题模型在实际中的应用造成不便.研究了三种不同需求分布条件下报童问题期望费用计算问题,所得出的关于期望费用计算公式具有简洁和便于实际应用的特点.     

带有模糊约束的房地产投资随机期望值模型

基于可信性理论,提出一类新的带有模糊约束的房地产投资随机期望值模型来处理房地产经济中的不确定性信息.另一方面,通过目标函数和可信性函数的一些性质将提出的房地产投资问题转化为一个等价的线性形式,从而可以利用经典的线性规划算法进行求解.最后,给出一个房地产投资问题的实例并通过Lindo软件进行求解.     

On a Constrained Optimal Rule for Classification with Unknown Prior Individual Group Membership

We describe a formal approach to constructing the optimal classification rule for classification analysis with unknown prior probabilities ofKmultivariate normal populations membership. This is done by suggesting a balanced design for the classification experiment and by constructing the optimal rule under the balanced design condition. The rule is characterized by a constrained minimization of total risk of misclassification; the constraint of the rule is constructed by a process of equalization among expected utilities ofKpopulation conditional densities. The efficacy of the suggested rule is examined through numerical studies. This indicates that dramatic gains in the accuracy of classification result can be achieved in the case where little is known about the relative population sizes.     

An interactive decision procedure with multiple attributes under risk

Consider a finite set of alternatives under risk which have multiple attributes. MARPI is an interactive computer-based procedure to find an efficient choice in the sense of linear expected utility. The choice is based on incomplete information about the decision maker's preferences which is elicited and processed in a sequential way. The information includes qualitative properties of the multivariate utility function such as monotonicity, risk aversion, and separability. Further, in case of an additively separable utility function, bounds on the scaling constants are elicited, and preferences (not necessarily indifferences) between sure amounts and lotteries are asked from the decision maker. The lotteries are Bernoulli lotteries generated by MARPI using special strategies. At every stage of the procedure the efficient set of alternatives is determined with respect to the information elicited so far.The procedure has been fully implemented on a PC. The paper exhibits the basic ideas of MARPI and some details of its implementation.