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

将要进行的研究将提供一个新的随机建模框架，一类在金融市场的均衡问题，并概述了这些模型的数学分析的新技术。 该项目的长期目标是建立一种通用方法，用于从市场原语（如金融代理人的效用函数和随机收入）以及公开信息的结构中指定股票价格模型。虽然主要工具包括随机分析，一般过程理论和有限加性概率，但对这些问题的分析也需要使用泛函和凸分析以及不动点理论的方法。 此外，其他几个纯粹的概率和随机分析项目，从不同方面出现的中心问题将被考虑。金融市场价格的形成是最有趣的和相关的问题之一，在数学和经济学的交叉。尽管投资者在金融环境中具有理性特征，但要预测股票、债券、商品或任何其他类别资产的未来价格是极其困难的。然而，这些工具的价格演变的定性性质可以使用数学工具进行研究，并且可以从容易观察到的原语中推断出大量关于它们的信息。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作。

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.