Stochastically ordered random variables with given marginal distributions are combined into a joint distribution preserving the ordering and the marginals using a maximum entropy formulation. A closed-form expression is obtained. An application is in default estimation for different portfolio...

A Bayesian approach to default rate estimation is proposed and illustrated using a prior distribution assessed from an experienced industry expert. The principle advantage of the Bayesian approach is the potential for coherent incorporation of expert information - crucial when data are scarce or...

Incorporation of expert information in inference or decision settings is often important, especially in cases where data are unavailable, costly or unreliable. One approach is to elicit prior quantiles from an expert and then to fit these to a statistical distribution and proceed according to...

Dependence among defaults both across assets and over time has proven to be an important characteristic of financial risk. A Bayesian approach to default rate estimation is proposed and illustrated using a prior distributions assessed from an experienced industry expert. Two extensions of the...

We show that the asymptotic mean of the log-likelihood ratio in a misspecified model is a differential geometric quantity that is related to the exponential curvature of Efron (1978), Amari (1982), and the preferred point geometry of Critchley et al. (1993, 1994). The mean is invariant with...