DEPARTMENT OF MATHEMATICAL SCIENCES

APPLIED AND COMPUTATIONAL MATHEMATICS SEMINAR

**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.

**Place:** Science and Technology Building I, 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