Universität Bielefeld

Institut für

Decision Theory

Our main interests lie in the following subfields of Decision Theory: DT4

Knightian Uncertainty in Economics and Finance

In many economic situations, the probabilities of uncertain outcomes are not known. In such a situation, we speak of Knightian or model uncertainty. A large decision-theoretic literature has been developed in the last two decades. We have applied this literature to several important economic problems. We axiomatically study time-consistency of coherent risk measures (the finance counterparts of Knightian preferences) in a paper in the mathematics journal Stochastic Processes and Their Applications (2004) and developed a general theory of optimal stopping under Knightian uncertainty (Econometrica 2009). With Xue Cheng (Chinese Academy of Sciences), we generalized the theory to continuous time (Mathematics and Financial Economics 2013). Frank Riedel and Tatjana Chudjakow studied the secretary or best choice problem in such a framework (Economic Theory, to appear). Frank Riedel and Linda Sass started a project on so-called Ellsberg games where players are allowed to use ambiguity in a strategic way, by using Ellsberg urns instead of randomizing devices (Theory and Decision, to appear). This led to a joint research project with Jean-Marc Tallon (Université Paris Panthéon?Sorbonne) that is funded by the German Research Foundation (DFG) and the French Research Foundation (ANR).

Risk Measures

Monetary risk measures aim to assess the risk of financial positions in amounts of money. As such, they play a fundamental role in the (future, better) regulation if financial markets. What has started as a purely axiomatic research agenda, has turned out to be useful for decision theory in general (in its relation to Knightian uncertainty models) and mechanism design (of financial regulation). Frank Riedel has clarified the structure of time consistent dynamic risk measures (Dynamic Coherent Risk Measures, Stochastic Processes and Applications, 2004). Optimal Stopping under such measures is investigated in the Econometrica paper Optimal Stopping with Multiple Priors (2009).

Judgment aggregation theory and applications

Arrovian aggregation theory, i.e. social choice theory in the tradition of Kenneth Arrow?s Social Choice and Individual Values (2nd ed. 1963), has moved towards ever greater generality during the past decade, culminating in a new literature in which the aggregation of sets of judgments, typically conceived as sets of propositions in some formal language, is investigated (Dietrich and List, Oxford Studies in Epistemology 2010). In recent papers, we have systematized a new approach to this field of judgment aggregation theory, in which we build on earlier work by Lauwers and Van Liedekerke (Journal of Mathematical Economics 1995) through introducing model theory (a branch of mathematical logic) as a principal tool of Arrovian social choice theory (Herzberg and Eckert, Journal of Philosophical Logic 2012; Herzberg and Eckert, Mathematical Social Sciences 2012). One of the chief advantages of our approach compared to other acounts of judgment aggregation theory lies in its greater expedience in relation to the analysis of economic (as opposed to political, judicial, or philosophical) aggregation problems. We focus on two sets of applications: Firstly, we study the possibility of Arrovian aggregation of preference orderings capturing ambiguity aversion (e.g. Herzberg, Economic Theory Bulletin 2013). Secondly, we examine Arrovian social-choice theoretic microfoundations for representative agents of macroeconomic models involving continuum-size populations (e.g. Herzberg, Journal of Mathematical Economics 2010).