Speaker:Harbir Lamba, Mathematics, George Mason University

Title: Modeling Imperfect Financial Markets

Abstract: The standard (efficient market) models of economics and mathematical finance make severe assumptions about the rationality, motivation and decision-making mechanisms of participants. However, their statistical properties differ significantly from those of real markets. I shall describe an alternative class of models within which many of the standard assumptions can be systematically weakened (ie. the efficient-market paradigm exists as a special case within this framework).

Briefly, the current `strategy' of a particular agent is defined by a pair of dynamic thresholds straddling the current price. When the price crosses either of these thresholds the agent switches investment position and a new pair of thresholds is generated. Such models are capable of robustly reproducing the most important stylized facts of financial markets, such as the apparent power-law distribution of the largest price-changes. Furthermore, the threshold dynamics can mimic different sources of investor motivation, running the gamut from purely rational information processing and inductive learning, through rational (but often undesirable!) behaviour induced by perverse incentives and moral hazards, to irrational psychological effects.

The model can be reformulated as a system of particles moving on a two-dimensional domain that switch state and are reinjected whenever a boundary is crossed. This abstraction helps clarify the question of which phenomena, when introduced into an otherwise efficient market, can cause significant asset mispricing. Finally we demonstrate a connection between these threshold models and the Olami-Feder-Christensen description of earthquakes.

No investment advice will be offered.

Time: Friday, December 5, 2008, 1:30-2:30 p.m.

Place: Science and Technology Building I, Room 242

Department of Mathematical Sciences
George Mason University
4400 University Drive, MS 3F2
Fairfax, VA 22030-4444
Tel. 703-993-1460, Fax. 703-993-1491