Year: 2018
Type: preprint
Abstract: For large systems of Brownian particles interacting through their ranks introduced in (Banner, Fernholz, Karatzas, 2005), the empirical cumulative distribution function satisfies a porous medium PDE. However, when we introduce a common noise, the limit is no longer deterministic. Instead, we show that this limit is a solution of a stochastic PDE related to this porous medium PDE. This stochastic PDE is somewhat similar to the equations developed for conservation laws with rough stochastic fluxes (Lions, Perthame, Souganidis, 2013).
Source: arXiv (Cornell University)
Authors: Kolli, Praveen, Sarantsev, Andrey
Institutions: University of Nevada, Reno, Carnegie Mellon University
Language: English
Subfield: Finance
Domain: Social Sciences
Open Access status: green
OpenAlex ID: W2950946373