Weighted Banzhaf values

The family of weighted Banzhaf values for cooperativen-person TU-games is studied. First we introduce the weighted Banzhaf value for an exogenously given vector of positive weights of the players. Then we give an axiomatic characterization of the class of all possible weighted Banzhaf values.     

A functional equation arising from ranked additive and separable utility

All strictly monotonic solutions of a general functional equation are determined. In a particular case, which plays an essential role in the axiomatization of rank-dependent expected utility, all nonnegative solutions are obtained without any regularity conditions. An unexpected possibility of reduction to convexity makes the present proof possible.

     

基于生活水平货币度量的助学贷款被助者的经济效益研究

随着国民经济的增长以及教育成本的提高,大学学费也相应逐年提高.但是我国还存在相当数量的贫困生.助学贷款是解决贫困生完成学业的重要途径.论文站在助学贷款被助者的立场上,将被助者获得的经济效益进行了具体的定量化分析.首先分别讨论了两期不考虑银行利息率和考虑银行利息率情况下,基于CES型效用函数的助学贷款被助者经济效益的计算模型,然后分析了如何计算多期银行利息率情况下贷款被助者的经济效益.最后针对被助群体进行实证分析、计算并得出结论.     

Revisiting the problem of integrability in utility theory

We revisit the problem of integrability in the consumer theory, focusing on the main difficulties. First, we look for a neat and simple local existence result, and then for a global solution. Second, observing that a utility function (or indirect utility function) cannot be determined uniquely, we propose a means to get a kind of uniqueness result. Our approach is coordinate-free and can be used both in the classical case of a finite-dimensional commodity space and in the case an infinite-dimensional model is adopted.     

A review of mathematical models in economic environmental problems

The paper presents a review of mathematical models used in economic analysis of environmental problems. This area of research combines macroeconomic models of growth, as dependent on capital, labour, resources, etc., with environmental models describing such phenomena like natural resources exhaustion or pollution accumulation and degradation. In simpler cases the models can be treated analytically and the utility function can be optimized using, e.g., such tools as the maximum principle. In more complicated cases calculation of the optimal environmental policies requires a computer solution. This revised version was published online in June 2006 with corrections to the Cover Date.     

能量收集传感器网络中改进的能耗管理方案研究

能量收集传感器平台为网络协议的设计开辟了新的领域。为了支持网络的运行,能耗率不得高于能量收集率,否则,传感器节点会最终耗尽它们的能量。与资源处于静态的传统网络资源分配问题相比,充电速率的时间可变性带来了新的挑战。在本文中,我们首先研究了一种基于高效对偶分解和次梯度策略的算法QuickFix,计算出数据采样率和路由。然而,再次充电发生波动时的时标可能会快于传统方法的收敛时间,进而导致电池断电和溢出,这会造成采样丢失和能量收集机会丢失。为了解决这一动态问题,我们提出一种本地算法SnapIt,通过对采集率进行调节以维持电池电量在目标水平上。基于TOSSIM模拟器的性能评估表明,QuickFix和SnapIt联合起来可以跟踪网络瞬时最优效用,同时维持电池电量处于目标水平。与基于余压的IFRC相比,本文方法使总体数据速率平均提升42%,同时显著提升了网络效用。     

New approach to optimal control of stochastic Volterra integral equations

ABSTRACT

We study optimal control of stochastic Volterra integral equations (SVIE) with jumps by using Hida-Malliavin calculus.

• We give conditions under which there exist unique solutions of such equations.

• Then we prove both a sufficient maximum principle (a verification theorem) and a necessary maximum principle via Hida-Malliavin calculus.

• As an application we solve a problem of optimal consumption from a cash flow modelled by an SVIE.

     

Pooling,pricing and trading of risks

Exchange of risks is considered here as a transferable-utility, cooperative game, featuring risk averse players. Like in competitive equilibrium, a core solution is determined by shadow prices on state-dependent claims. And like in finance, no risk can properly be priced merely in terms of its marginal distribution. Pricing rather depends on the pooled risk and on the convolution of individual preferences. The paper elaborates on these features, placing emphasis on the role of prices and incompleteness. Some novelties come by bringing questions about existence, computation and uniqueness of solutions to revolve around standard Lagrangian duality. Especially outlined is how repeated bilateral trade may bring about a price-supported core allocation.     

用预期效用理论单位三角形解释共同比率效应

本文提供一个新的视角来观察共同比率效应.这个悖论可以用期望效用理论和预期效用理论来解释.特别地,Machina(1987)在期望效用理论单位三角形比较一对彩票,共同比率效应形成一个悖论.在预期效用理论单位三角形中,效用函数无差异曲线保持平行,但是彩票的连线向内收敛,从而说明共同比率效应在预期效用理论可能是合理的,而不再是一个悖论.     

多维分数布朗运动环境下的最优投资组合问题

在分数布朗运动环境下,讨论了单资产多噪声情形下的最优投资组合问题.假定标的资产价格遵循多维分数布朗运动驱动的常系数随机微分方程,在给定效用函数分别为幂函数和对数效用函数条件下,得到了最优投资组合问题的显式解.