Financial Markets under Knightian Uncertainty

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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.