Semi-analytical solution of a McKean–Vlasov equation with feedback through hitting a boundary
Semi-analytical solution of a McKean–Vlasov equation with feedback through hitting a boundary
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McKean-Vlasov 方程的半解析解，通过触及边界进行反馈
DOI：
10.1017/s0956792519000342
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发表时间：
2018
影响因子：
1.9
通讯作者：
C. Reisinger
中科院分区：
文献类型：
--
作者：
A. Lipton;Vadim Kaushansky;C. Reisinger
本文研究了一个粒子系统的非线性扩散方程，其中公共漂移依赖于粒子在边界上的吸收率。我们提供了一个解释这个方程，这也是相关的过冷Stefan问题，作为一个结构性的信用风险模型，在一个大型的相互关联的银行系统中的违约传染。利用热势方法，我们导出了跃迁密度和吸收损失的耦合沃尔泰拉积分方程组。对于小的相互作用参数，给出了一个近似展开式。我们还提出了一个数值解算法，并进行计算测试。
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.
银行系统中出生和违约的动态传染
影响因子：
1
作者：
Ichiba, Tomoyuki;Ludkovski, Michael;Sarantsev, Andrey.
通讯作者：
Sarantsev, Andrey.