Unquantifiable Uncertainty

The importance and the potential dangers of model dependency, although known to the academic community for decades,have become abundantly clear during the 2008 financial crisis. Since then several methods have been developed... [ view full abstract ]

The importance and the potential dangers of model dependency, although known to the academic community for decades,have become abundantly clear during the 2008 financial crisis. Since then several methods have been developed to reduce this dependency. The (completely) model-independent approach delivers bounds and hedges that are valid in all cases. This is in fact the worst-case analysis of the problems. Although, in most cases, the results are too conservative, they provide valuable universal bounds. Robust finance uses models which are not based on one single (historical) probability measure.Instead a set of such measures used in an attempt to obtain answers that are robust to modelling assumptions. Mathematically, these studies raise interesting questions in the of theory stochastic processes. Main difficulty arises from the fact that the classical theory uses the reference measure significantly in its constructions.In the past decade, these questions have been studied with much success.The model-independent approach also made interesting connections to the classical Monge-Kantorovic optimal transport problem. From theoretical decision theory, all these studies are attempts to quantify instances of Knightian type uncertainties. In this talk, I survey the recent results in model-independent and robust finance in the context of Knightian uncertainty.