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General Equilibrium Theory and Mathematical Finance

© Universität Bielefeld

Our main interests lie in the following subfields of General Equilibrium Theory and Mathematical Finance:

Heterogeneous Agents (with applications to Asset Pricing)

While in the abstract theory individuals in an economy are allowed to have heterogeneous preferences (e.g. with respect to risk or delay), and while in empirical studies indeed preference heterogeneity has been well documented, in applied research this heterogeneity is not often addressed. Work on the implications of heterogeneity of risk-preferences on portfolio holdings and asset prices include Hara, Huang, and Kuzmics (2007, Journal of Economic Theory) and Hara, Huang, and Kuzmics (2011, Journal of Economic Theory). Heterogeneity plays also arole for the term structure of interest rates, a topic Frank Riedel studied in his thesis (Imperfect Information and Investor Heterogeneity in the Bond Market, Physica, 1998, Heterogeneous Time Preferences and Humps in the Yield Curve: The Preferred Habitat Theory Revisited, European Journal of Finance, 2004). He also studied heterogeneous expectations (Arrow-Debreu Equilibria With Asymptotically Heterogeneous Expectations Exist, Economic Theory, 2003).

Other-Regarding Preferences

In the past there were a lot of discussions on the new models of "other-regarding preferences" put forward in many behavioral papers. While these parametric preferences certainly do not resolve the issues raised by the experiments, it is certainly true that humans tend to be influenced by the well-being or the consumption choices of others. Paul Heidhues (now ESMT Berlin) and Frank Riedel thus set out to study this question in a reasonably general setting. This led to the insight that markets make people look selfish, even if they are not. In contrast to what is frequently to be found in newspapers, markets thus do not make people selfish, but they rather induce a behavior that is indistinguishable from selfish behavior. For material wealth, markets remain a good institution, but people are not necessarily happy about the inequal outcome. In such societies, the second welfare theorem does not hold true. As a consequence, social welfare redistribution is generally accepted, to give an example. As some other people were working on similar questions, we joined three papers to one, which finally appeared in the Review of Economic Studies (2011).

Equilibrium Foundations for Financial Markets and Asset Pricing

Finance needs sound economic foundations. An important part of our research is concerned with the general equilibrium foundations of financial markets. Publications include Existence of Arrow?Radner Equilibrium with Endogenously Complete Markets under Incomplete Information, Journal of Economic Theory, 2001, by Frank Riedel, and Optimal Consumption Choice under Uncertainty with Intertemporal Substitution, Annals of Applied Probability, 2001, with Peter Bank. With Frederik Herzberg, we have recently investigated potentially complete markets in continuous time (Existence of Financial Equilibria in Continuous Time with Potentially Complete Markets, Journal of Mathematical Economics 2013).

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