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 segments, where priors on the individual default probabilities are available and the stochastic ordering is agreeable to separate experts. The ME formulation allows an efficiency improvement over separate analyses.
Bayesian analysis stochastic dominance joint distributions risk management defaults small probability estimation