Modeling Portfolio Loss by Interval Distributions

Models for a continuous risk outcome has a wide application in portfolio risk management and capital allocation. We introduce a family of interval distributions based on variable transformations. Densities for these distributions are provided. Models with a random effect, targeting a continuous risk outcome, can then be fitted by maximum likelihood approaches assuming an interval distribution. Given fixed effects, regression function can be estimated and derived accordingly when required. This provides an alternative regression tool to the fraction response model and Beta regression model.