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

Alexander Lipton, Vadim Kaushansky and Christoph Reisinger

Papers from arXiv.org

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.

Date: 2018-08, Revised 2018-08
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