The Law of Large Numbers for self-exciting correlated defaults

被引：20

作者：

Cvitanic, Jaksa ^{[1
]}

Ma, Jin ^{[2
]}

Zhang, Jianfeng ^{[2
]}

机构：

[1] CALTECH, Pasadena, CA 91125 USA

[2] USC Dept Math, Los Angeles, CA 90089 USA

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2012年 / 122卷 / 08期

基金：

美国国家科学基金会;

关键词：

Self-exciting; Correlated defaults; Credit risk; Law of Large Numbers; CREDIT CONTAGION;

D O I：

10.1016/j.spa.2012.04.003

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We consider a model of correlated defaults in which the default times of multiple entities depend not only on common and specific factors, but also on the extent of past defaults in the market, via the average loss process, including the average number of defaults as a special case. The paper characterizes the average loss process when the number of entities becomes large, showing that under some monotonicity conditions the limiting average loss process can be determined by a fixed point problem. We also show that the Law of Large Numbers holds under certain compatibility conditions. (C) 2012 Elsevier B.V. All rights reserved.

引用

页码：2781 / 2810

页数：30

共 22 条

[1]

Bielecki T., 2002, CREDIT RISK MODELING

[2] A general formula for valuing defaultable securities [J].