AMC-SS: Stochastic Modeling and Methods in Financial Equilibrium Theory

即将进行的研究将为金融市场中的一类均衡问题提供一个新的随机建模框架，并勾勒出对这些模型进行数学分析的新技术。该项目的长期目标是建立一种通用的方法，用于从市场原语(如效用函数和金融代理的随机收入)以及公开可用信息的结构中指定股票价格模型。虽然主要的工具包括随机分析、一般过程理论和有限可加概率，但对这类问题的分析也需要使用泛函分析、凸分析和不动点理论的方法。此外，还将考虑从中心问题的各个方面出现的其他几个纯粹的概率和随机分析项目。金融市场的价格形成是数学和经济学交叉中最有趣和最相关的问题之一。尽管投资者在金融环境中具有理性特征，但对股票、债券、大宗商品或任何其他类别资产的未来价格进行预测是极其困难的。然而，这些工具的价格演化的定性性质可以用数学工具来研究，而且关于它们的大量信息可以从容易观察到的原语中推断出来。这些知识可以导致更好的监管和提高金融体系的效率，以及更好地了解我们经济的整体运行情况。

The research to be performed will provide a new stochastic modeling framework for a class of equilibrium problems in financial markets, and outline a novel technique for a mathematical analysis of those models. The project's long-term goal is to build a general methodology for the specification of models of stock prices from market primitives such as utility functions and the random income of financial agents, and the structure of publicly available information. While the main tools include stochastic analysis, general theory of processes and finitely-additive probability, the analysis of such problems requires the use of methods from functional and convex analysis and fixed-point theory, as well. Moreover, several other purely probabilistic and stochastic-analytic projects which emerge from various aspects of the central problem will be considered.Formation of prices in financial markets is one of the most interesting and relevant problems at the intersection of mathematics and economics. Despite the rational character of investors in financial environment, it is extremely difficult to predict future prices of stocks, bonds, commodities or any other class of assets. However, the qualitative properties of the price-evolution of these instruments can be studied using mathematical tools and a great deal of information about them can be deduced from readily observable primitives. Such knowledge can lead to a better regulation and the increased efficiency of the financial system, as well as to a better understanding of the overall functioning of our economy.