Statistical Foundations of Actuarial Learning and its Applications

Abstract

The aim of this manuscript is to provide the mathematical and statistical foundations of actuarial learning. This is key to most actuarial tasks like insurance pricing, product development, claims reserving and risk management. The basic approach to these tasks is regression modeling. This manuscript describes the exponential dispersion family which is the most commonly used family of distributions in actuarial modeling. It discusses model fitting and parameter estimation using classical tools from mathematical statistics. It then introduces the crucial tools for prediction and forecast evaluation. Based on these statistical concepts various regression models are studied such as generalized linear models, mixture models and neural network regression models. We explore these modeling approaches from a theoretical and a practical viewpoint on publicly available data and we discuss their applications to insurance modeling. This involves model fitting using Fisher's scoring method, gradient descent algorithms or the expectation-maximization algorithm, model selection, parameter selection, regularization, etc.