Journal of Applied Mathematics
Volume 2011 (2011), Article ID 354171, 28 pages
http://dx.doi.org/10.1155/2011/354171
Research Article

Sample-Path Large Deviations in Credit Risk

V. J. G. Leijdekker,1,2 M. R. H. Mandjes,1,3,4 and P. J. C. Spreij1

1Korteweg-de Vries Institute for Mathematics, University of Amsterdam, P.O. Box 94248, 1090 GE Amsterdam, The Netherlands
2ABN AMRO, HQ2057, Gustav Mahlerlaan 10, 1082 PP Amsterdam, The Netherlands
3EURANDOM, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
4CWI, P.O. Box 94079, 1090 GB Amsterdam, The Netherlands

Received 5 July 2011; Accepted 20 September 2011

Academic Editor: Ying U. Hu

Copyright © 2011 V. J. G. Leijdekker et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The event of large losses plays an important role in credit risk. As these large losses are typically rare, and portfolios usually consist of a large number of positions, large deviation theory is the natural tool to analyze the tail asymptotics of the probabilities involved. We first derive a sample-path large deviation principle (LDP) for the portfolio's loss process, which enables the computation of the logarithmic decay rate of the probabilities of interest. In addition, we derive exact asymptotic results for a number of specific rare-event probabilities, such as the probability of the loss process exceeding some given function.