Financial institutions form multilayer networks by engaging in contracts with each other and by holding exposures to common assets. As a result, the default probability of one institution depends on the default probability of all of the other institutions in the network. Here, we show how small errors on the knowledge of the network of contracts can lead to large errors in the probability of sy...

This paper presents statistical default logic, an expansion of classical (i.e., Reiter) default logic that allows us to model common inference patterns found in standard inferential statistics, including hypothesis testing and the estimation of a populations mean, variance and proportions. The logic replaces classical defaults with ordered pairs consisting of a Reiter default in the first coord...

We introduce an infectious default and recoverymodel forN obligors. Obligors are assumed to be exchangeable and their states are described by N Bernoulli random variables Si(i = 1, · · · , N). They are expressed by multiplying independent Bernoulli variables Xi, Yij , Y ′ ij , and default and recovery infections are described by Yij and Y ′ ij . We obtain the default probability function P (k) ...

For a given filtered probability space (Ω,F,P), where F = (Ft)t≥0 is a filtration, an F-adapted continuous increasing process Λ and a positive P-F local martingale N such that Zt := Nte−Λt ≤ 1, t ≥ 0, we construct a model of default time, i.e., a probability measure QZ and a random time τ on an extension of (Ω,F,P), such that Q[τ > t|Ft] = Zt, t ≥ 0. The probability QZ is linked with the well-k...

We present a semantics for adding uncertainty to conditional logics for default reasoning and be­ lief revision. We are able to treat conditional sen­ tences as statements of conditional probability, and express rules for revision such as "If A were believed, then B would be believed to degree p." This method of revision extends conditional­ ization by allowing meaningful revision by sen­ tence...