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What is Learnable in Valiant's Theory of the Learnable? 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A nonparametric urn-based approach to interacting failing systems with an application to credit risk modeling
Pasquale Cirillo, Jürg Hüsler, Pietro Muliere · 2010-10-18 · via math.ST updates on arXiv.org

In this paper we propose a new nonparametric approach to interacting failing systems (FS), that is systems whose probability of failure is not negligible in a fixed time horizon, a typical example being firms and financial bonds. The main purpose when studying a FS is to calculate the probability of default and the distribution of the number of failures that may occur during the observation period. A model used to study a failing system is defined default model. In particular, we present a general recursive model constructed by the means of inter- acting urns. After introducing the theoretical model and its properties we show a first application to credit risk modeling, showing how to assess the idiosyncratic probability of default of an obligor and the joint probability of failure of a set of obligors in a portfolio of risks, that are divided into reliability classes.

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