397 RISK, MODEL RISK, AND KNIGHTIAN UNCERTAINTY: ON THE ROLE OF PROBABILITY IN FINANCE

Hans Föllmer, Humboldt University, Germany

Over the last decades, advanced probabilistic methods have played an increasing role in Finance, both in Academia and in the financial industry. In view of the recent financial crisis it has been asked to which extent the use of such methods has been part of the problem. We review and comment on some of the answers, ranging from "don't blame the quants" to "misplaced reliance of sophisticated maths" and "the financial crisis: a question of guilt", or of "structural irresponsibility". We will then focus on the foundational issue of "Knightian uncertainty" raised in "The Turner Review: A regulatory response to the global banking crisis" of the British Financial Services Authority. This will be illustrated by the problem of quantifying financial risk. We discuss recent advances in the theory of convex risk measures, in particular the connection to robust preferences which extend the classical paradigm of expected utility. This leads to a robustification of classical problems of optimal portfolio choice, where model ambiguity is taken into account explicitely.