Semi-analytical solution of a McKean–Vlasov equation with feedback through hitting a boundary

Author: 

Kaushansky, V
Reisinger, C
Lipton, A

Publication Date: 

16 December 2019

Journal: 

European Journal of Applied Mathematics

Last Updated: 

2020-02-05T12:46:10.57+00:00

DOI: 

10.1017/S0956792519000342

page: 

1-34

abstract: 

© 2019 Cambridge University Press. In this paper, we study the nonlinear 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 of this equation, which is also related to the supercooled Stefan problem, 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.

Symplectic id: 

1072636

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article