Economic Models with Infinitely Many Commodities

该项目开发了具有无限数量商品的市场的新经济模型。这些模型用于研究大量企业的垄断竞争、不确定性下金融市场的动态、市场数学模型的基础以及数学经济理论中的其他难题。更具体地说，在项目的第一部分中，开发了一个模型，其中企业足够小，以至于每个企业对其他企业的影响可以忽略不计，但在均衡状态下，活跃企业收取的价格高于完全竞争价格，并可能获得正垄断利润。这个模型将比现有的经济模型更现实，在现有的经济模型中，企业的垄断力量随着它们与市场相比变小而消失。第二部分是不完全市场连续时间随机模型的发展。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索赔市场实际上是缺失的。连续时间框架允许研究者将他的工作与金融模型联系起来，并解决诸如：频繁交易是否会提高效率？

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?