Financial Markets under Knightian Uncertainty

近年来，奈特不确定性(模型不确定性)问题已成为金融经济学和决策理论中的一个重要主题。关于奈特不确定性下的决策，已经在经济方面发展了一个庞大而成功的理论，并在数学方面补充了大量关于风险衡量的文献。这两个研究方向都强调需要处理敏感的建模假设。本项目的目的是在“无模型”和“多重优先”的框架下，发展奈特不确定性下的金融市场均衡理论。从概念上讲，我们的目标是澄清概率假设在金融中的作用。在连续时间金融的多重先验框架中，主要的技术挑战出现了，因为人们必须使用相互单一的概率度量，这些度量描述了奈特不确定性下的不同“场景”。我们将把随机微积分的最新发展应用到一般均衡理论中，研究奈特不确定性下完全和不完全金融市场的存在性和结构性质。

In recent years, the issue of Knightian uncertainty (model uncertainty) has emerged as a major theme in financial economics and decision theory. A large and successful theory of decision making under Knightian uncertainty has been developed on the economic side, complemented by a rich literature on risk measures on the mathematical side. Both research strands emphasize the need to deal with sensitive modeling assumptions. The present project aims to develop the equilibrium theory of financial markets under such Knightian uncertainty, both in a "model--free" and a "multiple prior" framework. Conceptually, we aim to clarify the role of probabilistic assumptions in finance. In the multiple prior framework for continuous--time finance, major technical challenges emerge as one has to work with mutually singular probability measures that describe different "scenarios" under Knightian uncertainty. We will apply recent developments in stochastic calculus to general equilibrium theory and study existence and structural properties of complete and incomplete financial markets under Knightian uncertainty.