Convexity and Duality in the Economics of Financial Equilibrium

Abstract

In classical models of economic equilibrium with markets of
goods, agents maximize quasi-concave utility subject to budget constraints
based on the value of their initial holdings.  When financial markets are
added, there are serious complications because of uncertainties over
future states which the model must reflect. In that context, the existence of
prices that bring supply and demand into balance is far from assured, and
current theory is unsatisfying.
However, strong results about the existence of equilibrium have recently
been obtained by requiring utility functions to be concave, instead of just
quasi-concave, while taking a new approach to “money”.  Concavity allows
Lagrangian duality to generate underlying compactness in variational
inequality representation of equilibrium.  In combination with the “money”
feature, it greatly simplifies the assumptions needed on the initial
holdings of the agents.

Posted on Oct 24, 2013 in Optimization and Equilibrium, Seminars