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摘要
The current financial crisis motivates the study of correlated defaults in financial systems. In this paper we focus on such a model, which is based on Markov random fields. This is a probabilistic model in which uncertainty in default probabilities incorporates experts' opinions on the default risk (based on various credit ratings). We consider a bilevel optimization model for finding an optimal recovery policy: which companies should be supported given a fixed budget. This is closely linked to the problem of finding a maximum likelihood estimator of the defaulting set of agents, and we show how to compute this solution efficiently using combinatorial methods. We also prove properties of such optimal solutions and give a practical procedure for estimation of model parameters. Computational examples are presented, and experiments indicate that our methods can find optimal recovery policies for up to about 100 companies. The overall approach is evaluated on a real-world problem concerning the major banks in Scandinavia and public loans. To our knowledge, this is a first attempt to apply combinatorial optimization techniques to this important and expanding area of default risk analysis. Subject classifications: financial models; discrete optimization; bilevel programming; Markov random field. Area of review: Financial Engineering. History: Received October 2009; revisions received February 2010, December 2010, March 2011; accepted April 2011. Published online in Articles in Advance November 20, 2012.
- 出版日期2012-12
