Integer and combinatorial optimization
Integer and combinatorial optimization
Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
A bilevel model of taxation and its application to optimal highway pricing
Management Science
Large-Scale Integer Programs in Image Analysis
Operations Research
Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images
IEEE Transactions on Pattern Analysis and Machine Intelligence
Lagrangian-based methods for finding MAP solutions for MRF models
IEEE Transactions on Image Processing
Sequential Importance Sampling and Resampling for Dynamic Portfolio Credit Risk
Operations Research
| Hi-index | 0.00 |
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.