Department of Mathematics
Indian Institute of Science
Bangalore 560 012
SEMINAR
Speaker |
: |
Dr.Soumik Pal |
Affiliation |
: |
University of Washington, Seattle
|
Subject Area |
: |
Mathematics
|
Venue |
: |
Lecture Hall - I, Dept of Mathematics
|
Time |
: |
4 pm
|
Date |
: |
August 4,2009 (Tuesday) |
Title |
: |
Interacting diffusion models and the effect of size |
Abstract | : |
Consider a multidimensional
diffusion model where the drift and the diffusion coefficients for
individual coordinates are functions of the relative sizes of their current
value compared to the others. Two such models were introduced by Fernholz
and Karatzas as models for equity markets to reflect some well-known
empirically observed facts. In the first model, called 'Rank-based', the
time-dynamics is determined by the ordering in which the coordinate values
can be arranged at any point of time. In the other, named the
'Volatility-stabilized', the parameters are functions of the ratio of the
current value to the total sum over all coordinates. We show some remarkable
properties of these models, in particular, phase transitions and infinite
divisibility. Relationships with existing models of queueing, dynamic spin
glasses, and statistical genetics will be discussed. Part of the material is
based on separate joint work with Sourav Chatterjee and Jim Pitman.
|