英文标题：
《Semi-analytical solution of a McKean-Vlasov equation with feedback
  through hitting a boundary》
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作者：
Alexander Lipton, Vadim Kaushansky, and Christoph Reisinger
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最新提交年份：
2018
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英文摘要：
  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.
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中文摘要：
在本文中，我们研究了与粒子系统相关的非线性扩散方程，其中共同漂移取决于粒子在边界处的吸收速率。我们将其解释为在大型互联银行系统中存在违约传染的结构性信贷风险模型。利用热势方法，我们导出了跃迁密度和吸收损耗的Volterra积分方程组。对于一个小的相互作用参数，给出了一个展开近似。我们还提出了一种数值求解算法并进行了计算测试。
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分类信息：

一级分类：Mathematics        数学
二级分类：Numerical Analysis        数值分析
分类描述：Numerical algorithms for problems in analysis and algebra, scientific computation
分析和代数问题的数值算法，科学计算
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一级分类：Quantitative Finance        数量金融学
二级分类：Computational Finance        计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
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