无套利预算对应的连续性

当消费者的偏好是凸的 (不一定严格凸 )时 ,不完全市场的预算约束是价格单纯形与Grassman流形的乘积空间到商品空间的非线性集合值映射 ,简称为预算对应 .为了研究该模型的一般经济均衡的存在性 ,作者研究了无套利预算对应的性质 ,得到如下主要结果 :无套利预算对应是连续的 .     

Fast heuristics for the Steiner tree problem with revenues,budget and hop constraints

This article describes and compares three heuristics for a variant of the Steiner tree problem with revenues, which includes budget and hop constraints. First, a greedy method which obtains good approximations in short computational times is proposed. This initial solution is then improved by means of a destroy-and-repair method or a tabu search algorithm. Computational results compare the three methods in terms of accuracy and speed.     

Convex risk functionals: Representation and applications

We introduce the family of law-invariant convex risk functionals, which includes a wide majority of practically used convex risk measures and deviation measures. We obtain a unified representation theorem for this family of functionals. Two related optimization problems are studied. In the first application, we determine worst-case values of a law-invariant convex risk functional when the mean and a higher moment such as the variance of a risk are known. Second, we consider its application in optimal reinsurance design for an insurer. With the help of the representation theorem, we can show the existence and the form of optimal solutions.     

Cut problems in graphs with a budget constraint

We study budgeted variants of classical cut problems: the Multiway Cut problem, the Multicut problem, and the k-Cut problem, and provide approximation algorithms for these problems. Specifically, for the budgeted multiway cut and the k-cut problems we provide constant factor approximation algorithms. We show that the budgeted multicut problem is at least as hard to approximate as the sparsest cut problem, and we provide a bi-criteria approximation algorithm for it.     

Demand functions and reflexivity

In the theory of ordered spaces and in microeconomic theory two important notions, the notion of the base for a cone which is defined by a continuous linear functional and the notion of the budget set are equivalent. In economic theory the maximization of the preference relation of a consumer on any budget set defines the demand correspondence which at any price vector indicates the preferred vectors of goods and this is one of the fundamental notions of this theory. Contrary to the finite-dimensional economies, in the infinite-dimensional ones, the existence of the demand correspondence is not ensured. In this article we show that in reflexive spaces (and in some other classes of Banach spaces), there are only two classes of closed cones, i.e. cones whose any budget set is bounded and cones whose any budget set is unbounded. Based on this dichotomy result, we prove that in the first category of these cones the demand correspondence exists and that it is upper hemicontinuous. We prove also a characterization of reflexive spaces based on the existence of the demand correspondences.     

Aggregate preferred correspondence and the existence of a maximin REE

A general model of a pure exchange differential information economy is studied. In this economic model, the space of states of nature is a complete probability measure space, the space of agents is a finite measure space, and the commodity space is the Euclidean space. Under some appropriate and standard assumptions on agents' characteristics, results on continuity and measurability of the aggregate preferred correspondence similar to that of Aumann [8] are established. These results together with other techniques are then employed to prove the existence of a maximin rational expectations equilibrium (maximin REE) of the economic model.     

Bayesian optimal knapsack procurement

A budget-constrained buyer wants to purchase items from a shortlisted set. Items are differentiated by observable quality and sellers have private reserve prices for their items. The buyer’s problem is to select a subset of maximal quality. Money does not enter the buyer’s objective function, but only his constraints. Sellers quote prices strategically, inducing a knapsack game. We report the Bayesian optimal mechanism for the buyer’s problem. We find that simultaneous take-it-or-leave-it offers are interim optimal.     

A model to enhance the reliability of the serial parallel systems with component mixing

System reliability, especially for serial parallel systems, has attracted much attention in recent years. Redundancy allocation is a technique to increase the reliability of the serial parallel systems. Supplying redundant components depends on some restrictions such as available budget, weight, space, etc. This paper proposes a new model for redundancy allocation problems (RAPs) by considering discount policy. The proposed model attempts to maximize the reliability of a system by gathering various components where there are some limitations on budgeting. We present two models with different assumptions including all unit discount and incremental discount strategies. The resulted formulations are nonlinear integer models and categorized as NP-hard. Therefore, some heuristics and meta-heuristics are designed to solve the resulted models, efficiently.     

The multi-product newsboy problem with supplier quantity discounts and a budget constraint

This paper considers the multi-product newsboy problem with both supplier quantity discounts and a budget constraint, while each feature has been addressed separately in the literature. Different from most previous nonlinear optimization models on the topic, the problem is formulated as a mixed integer nonlinear programming model due to price discounts. A Lagrangian relaxation approach is presented to solve the problem. Computational results on both small and large-scale test instances indicate that the proposed algorithm is extremely effective for the problem. An extension to multiple constraints and preliminary computational results are also reported.