On Knightian uncertainty models : optimal behavior in presence of model uncertainty

Chudjakow T. On Knightian uncertainty models : optimal behavior in presence of model uncertainty. Bielefeld (Germany): Bielefeld University; 2010.In the framework of Knightian uncertainty more precisely in the model introduced by Epstein and Schneider (2003) 3 different questions concerning the optimal behavior in presence of ambiguity are studied. The first part reformulates and solves Best Choice Problems in the multiple prior framework: An ambiguity averse decision maker aims to choose the best among a fixed number of applicants that appear sequentially in a random order. It shows that as in the classical case the derived stopping strategy is simple. However, ambiguity can lead to substantial differences to the classical threshold rule leading to later or earlier stopping. Second part analyzes several exotic options of American style in a multiple prior setting. It studies the optimal exercise strategy from the perspective of an ambiguity averse buyer in a discrete market model. The section provides the explicit form of worst-case measure for different classes of exotic options exploiting the observation that the options can be decomposed in simpler event-driven claims. The last part analyzes a static partial equilibrium model where the agents are not only heterogeneous in their beliefs about the return on risky assets but also in their attitude to it. While some agents in the economy are subjective utility maximizers others behave ambiguity averse in the sense of Knight (1921). If ambiguity averse agents meet overly optimistic subjective utility maximizers in the market lower equity premia can arise in the equilibrium than in a purely subjective utility framework