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The Law of Large Numbers for self-exciting correlated defaults

Cvitanić, Jakša and Ma, Jin and Zhang, Jianfeng (2012) The Law of Large Numbers for self-exciting correlated defaults. Stochastic Processes and their Applications, 122 (8). pp. 2781-2810. ISSN 0304-4149. doi:10.1016/j.spa.2012.04.003. https://resolver.caltech.edu/CaltechAUTHORS:20120813-111328071

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Abstract

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.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1016/j.spa.2012.04.003DOIArticle
http://www.sciencedirect.com/science/article/pii/S0304414912000646PublisherArticle
ORCID:
AuthorORCID
Cvitanić, Jakša0000-0001-6651-3552
Additional Information:© 2012 Elsevier B.V. Received 28 February 2011; received in revised form 2 November 2011; accepted 3 April 2012; Available online 12 April 2012. The first author’s research was supported in part by NSF grants DMS #06-31298 and #10- 08219. The second author’s research was supported in part by NSF grants DMS #08-06017 and #11-06853. The third author’s research was supported in part by NSF grant DMS #10-08873.
Funders:
Funding AgencyGrant Number
NSFDMS-06-31298
NSFDMS-10-08219
NSFDMS-08-06017
NSFDMS-11-06853
NSFDMS-10-08873
Subject Keywords:Self-exciting; Correlated defaults; Credit risk; Law of Large Numbers
Issue or Number:8
Classification Code:MSC: 91G40; 60H10; 91G80
DOI:10.1016/j.spa.2012.04.003
Record Number:CaltechAUTHORS:20120813-111328071
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20120813-111328071
Official Citation:Jakša Cvitanić, Jin Ma, Jianfeng Zhang, The Law of Large Numbers for self-exciting correlated defaults, Stochastic Processes and their Applications, Volume 122, Issue 8, August 2012, Pages 2781-2810, ISSN 0304-4149, 10.1016/j.spa.2012.04.003. (http://www.sciencedirect.com/science/article/pii/S0304414912000646)
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:33126
Collection:CaltechAUTHORS
Deposited By:INVALID USER
Deposited On:13 Aug 2012 18:28
Last Modified:09 Nov 2021 21:32

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