Much of actuarial science deals with the analysis and management of financial risk. In this new text we address the topic of loss models, traditionally called risk theory by actuaries, including the estimation of such models from sample data. The theory of survival models is addressed in other texts, including the ACTEX work entitled Models for Quantifying Risk which might be considered a companion text to this one. In Risk Models and Their Estimation we consider as well the estimation of survival models, in both tabular and parametric form, from sample data