DEPARTMENT OF MATHEMATICAL SCIENCES

APPLIED AND COMPUTATIONAL MATHEMATICS SEMINAR

**Speaker:** Harbir Lamba, George Mason University

**Title: ***
Far-from-Equilibrium Dynamics in Economic and Financial Systems
*

**Abstract:**
Most models in mainstream economics and finance, either
explicitly or implicitly, assume that the underlying system is dominated
by equilibrating forces, ie that the evolution of such systems is
mostly an adiabatic response to exogenous shocks/information. However,
such models have routinely failed to predict, recognise or even explain
(in any consistent manner) spectacular and extremely damaging system-wide
crises. Indeed, given the way that such models interact with the systems
they are describing they may even have caused the crises.

The talk will focus on perhaps the two most important disequilibrating factors that are ignored, or treated simplistically, by such models. The first are `frictions' that prevent or discourage agents from acting instantaneously and thus introduce history-dependence. The second is the lack of independence between agents' actions due to, for example, correlated trading strategies, widespread misconceptions, or perverse incentives.

I will present an asset-pricing model that (using ideas from the Preisach description of magnetic hysteresis) can incorporate both of the above effects (and others) in a plausible and consistent manner. The resulting mathematical model is a pair of coupled stochastic PDEs with unusual non-local boundary conditions. When agents act independently the aggregate system reduces to geometric Brownian motion which allows us to numerically investigate the stability of this equilibrium solution. At the other extreme, I will demonstrate a link between Queueing Theory and the cascading processes that mark the rapid bursting of market bubbles.

If there is time I will also show how a similar methodology can
be applied to investigate the validity of other equilibrium models such
as the DSGE models of macroeconomics and those assumed-to-exist
supply-demand curves from Economics 101.

**Time:** Friday, Apr. 13, 2012, 1:30-2:30 p.m.

**Place:** Science and Tech 1, Room 242

Department of Mathematical Sciences

George Mason University

4400 University Drive, MS 3F2

Fairfax, VA 22030-4444

http://math.gmu.edu/

Tel. 703-993-1460, Fax. 703-993-1491