Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1155722 | Stochastic Processes and their Applications | 2013 | 17 Pages |
Abstract
We investigate the behavior of systems of interacting diffusion processes, known as volatility-stabilized market models in the mathematical finance literature, when the number of diffusions tends to infinity. We show that, after an appropriate rescaling of the time parameter, the empirical measure of the system converges to the solution of a degenerate parabolic partial differential equation. A stochastic representation of the latter in terms of one-dimensional distributions of a time-changed squared Bessel process allows us to give an explicit description of the limit.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Mykhaylo Shkolnikov,