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Published August 2012 | public
Journal Article

The Law of Large Numbers for self-exciting correlated defaults

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.

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.

Additional details

Created:
August 22, 2023
Modified:
October 18, 2023