Semi-analytical solution of a McKean-Vlasov equation with feedback through hitting a boundary
Numerical Analysis
2018-08-28 v2 Computational Finance
Abstract
In this paper, we study the non-linear diffusion equation associated with a particle system where the common drift depends on the rate of absorption of particles at a boundary. We provide an interpretation as a structural credit risk model with default contagion in a large interconnected banking system. Using the method of heat potentials, we derive a coupled system of Volterra integral equations for the transition density and for the loss through absorption. An approximation by expansion is given for a small interaction parameter. We also present a numerical solution algorithm and conduct computational tests.
Keywords
Cite
@article{arxiv.1808.05311,
title = {Semi-analytical solution of a McKean-Vlasov equation with feedback through hitting a boundary},
author = {Alexander Lipton and Vadim Kaushansky and Christoph Reisinger},
journal= {arXiv preprint arXiv:1808.05311},
year = {2018}
}