We introduce new robust numerical methods, based on the minimum relative U−entropy (MRUE) principle, to estimate univariate probability density functions for power-law (fat-tailed) random variables. The semi-parametric models that we estimate via convex programming are flexible enough to...

We estimate joint stock return probability distributions for large portfolios of stocks via a method that can accommodate fat-tailed, dependent, covariates with an ill-conditioned covariance matrix. Our method strikes a balance between fidelity to the training data and regularization, with the...

A number of conditional transition probability models make use of side information - explanatory variable values known only initially and useful for predicting transitions of the variables of interest. For example, the Cox Proportional Hazard Model is used to provide future hazard arrival...

A number of researchers have used the Cox Proportional Hazard Model to estimate multi-period corporate default probabilities. By construction, models estimated in this manner have hazard ratios that are constant over time. We present evidence, drawn from historical data, indicating that...

We establish novel necessary and sufficient conditions for a particularly tractable concept of monotonic dependence of an exponential conditional probability model on its explanatory variables. We introduce convex programming methods to calibrate such models (which are monotone in conditional...

We estimate real-world private firm default probabilities over a fixed time horizon,conditioned on a vector of explanatory variables, which include financial ratios, economic indicators, and market prices. To estimate our model, we apply a recently developed method from statistical learning...

We present some general results pertaining to Most Entropic Copulas (MECs), and describe the connection between MECs and a special type of Markov random field model. We also describe a fundamental, new, MEC, the Spearman Copula, which is, in some sense, the simplest nontrivial MEC, and present...

We introduce new methods to generate finite representative collections of plausible yet severe scenarios. We apply these methods to generate single- obligor credit risk scenarios and demonstrate, via numerical experiments, that with respect to certain performance measures, our method is better...

We present new, tractable methods to impute missing values based on conditional probability density functions that we estimate via copula and mixture models. Our methods exploit known analytical results concerning conditional distributions for the Arellano-Valle and Bolfarine's generalized...