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...

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...

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...

Accurate credit-granting decisions are crucial to the efficiency of the decentralized capital allocation mechanisms in modern market economies. Credit bureaus and many financial institutions have developed and used credit-scoring models to standardize and automate, to the extent possible, credit...

Capital allocation decisions are made on the basis of an assessment of creditworthiness. Default is a rare event for most segments of a bank's portfolio and data information can be minimal. Inference about default rates is essential for efficient capital allocation, for risk management and for...

Default is a rare event, even in segments in the midrange of a bank's portfolio. Inference about default rates is essential for risk management and for compliance with the requirements of Basel II. Most commercial loans are in the middle-risk categories and are to unrated companies. Expert...