On dynamic Knightian uncertainty models : time-consistency and optimal behavior

In the framework of Knightian uncertainty more precisely in the model introduced by Epstein and Schneider 3 different questions concerning the aspect of time-consistency, in the sense of m-stability or rectangularity, are studied.The first part describes an alternative description of time-consistent sets in the special framework of finite decision trees. It shows how the characteristics of time-consistent sets of measures can be expressed with the help of density functions, more precisely density generators, and vice versa.The second part discusses a duality approach for optimal decisions under uncertainty. It gives an answer to the question: when is it possible to interchange the order of minimizing with respect to distributions with the maximization over actions.The third and final part deals with a concept of learning under uncertainty. With the aim of explaining shifts in risk assessments over time the first approach is to explicitly construct an appropriate risk measure. Showing that this cannot be done in a straightforward way, the second and more important approach takes the existence of such a risk measure for granted and shows what happens in the course of time as information increases. This second approach is a generalization of the Blackwell and Dubins Theorem to coherent as well as convex risk measures.