Economic Models with Infinitely Many Commodities

这个项目开发了具有无限数量的商品的市场的新的经济模型。这些模型被用来研究大量企业的垄断竞争、不确定条件下的金融市场动态、市场数学模型的建立以及其他数学经济理论中的难题。更具体地说，在项目的第一部分，建立了一个模型，在该模型中，企业足够小，使得每个企业对其他企业的影响可以忽略不计，但在均衡情况下，活跃的企业收取的价格高于完全竞争价格，可能获得正垄断利润。这种模型将比现有的经济模型更现实，在现有的经济模型中，随着企业的垄断力量与市场相比变得更小，垄断力量就会消失。第二部分是不完全市场的连续时间随机模型的发展。具有不完全市场的随机模型是有用的，因为在现实世界中，不可能完全防范不确定性，因为许多期货和或有债权市场实际上是缺失的。连续时间框架允许调查者将他的工作与金融模型联系起来，并解决这样的问题：频繁的交易是否会带来效率？

This project develops new economic models of markets with an infinite number of commodities. These models are used to study monopolistic competition with large numbers of firms, the dynamics of financial markets under uncertainty, the foundations of mathematical models of markets and other difficult problems in mathematical economic theory. More specifically, in the first part of the project a model is developed in which firms are sufficiently small so that each firm's effect on other firms is negligible, yet in equilibrium, active firms charge more than the perfectly competitive price and may make positive monopoly profits. This model would be more realistic than existing economic models in which the monopoly power of firms disappears as they become small in comparison to the market. The second part consists of the development of continuous time stochastic models of incomplete markets. Stochastic models with incomplete markets are useful because in the real world it is impossible to completely insure against uncertainty because many futures and contingent claims markets are in fact missing. The continuous time framework allows the investigator to relate his work to financial models and to address such questions as: does frequent trading lead to efficiency?