Work

Multiple collisions in systems of competing Brownian particles

Year: 2017

Type: article

Abstract: Consider a finite system of competing Brownian particles on the real line. Each particle moves as a Brownian motion, with drift and diffusion coefficients depending only on its current rank relative to the other particles. We find a sufficient condition for a.s. absence of a total collision (when all particles collide) and of other types of collisions, say of the three lowest-ranked particles. This continues the work of Ichiba, Karatzas and Shkolnikov [Probab. Theory Related Fields 156 (2013) 229–248] and Sarantsev (2016).

Source: Bernoulli

DOI: 10.3150/16-bej869

Authors: Cameron Bruggeman, Andrey Sarantsev

Institutions: Columbia University, University of California, Santa Barbara

Language: English

Topic: Stochastic processes and financial applications

Subfield: Finance

Field: Economics, Econometrics and Finance

Domain: Social Sciences

Open Access status: bronze

Funder: National Science Foundation

Awards: Eigenvectors of random graphs, random matrices and triple collisions, Eigenvectors of random graphs & diffusions on simplices, Systemic Risk and Nonlinear Problems in Financial Mathematics, Stochastic Controls, Portfolios, and Competing Particle Systems