Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
10527285 | Stochastic Processes and their Applications | 2012 | 18 Pages |
Abstract
We study the limiting behavior of the empirical measure of a system of diffusions interacting through their ranks when the number of diffusions tends to infinity. We prove that under certain assumptions the limiting dynamics is given by a McKean-Vlasov evolution equation. Moreover, we show that the evolution of the cumulative distribution function under the limiting dynamics is governed by the generalized porous medium equation with convection. The implications of the results for rank-based models of capital distributions in financial markets are also explained.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Mykhaylo Shkolnikov,