MSc Stats Defence: Generalized additive models for dependent frequency and severity of insurance claims

CANDIDATE:  TINGTING CHEN

ABSTRACT:

This thesis develops a new approach to risk analysis with a focus on property and casualty insurance industry applications. It examines the problem of accurately estimating the expected value and variance of the aggregate claims for each policyholder, as well as the prediction intervals of the estimated mean aggregate claims to quantify the risk. Through an appropriate premium statistical model, an insurer can find its particular niche markets to operate both competitively and profitably. To this end, the framework of generalized linear models (GLMs) for aggregate claims under both independent and dependent assumptions is extended to a structure of frequentist generalized additive models (GAMs) based on cubic penalized regression splines with a cardinal spline basis, which allows more flexible nonlinear and/or nonparametric trend terms for the marginal claim frequency and conditional claim severity models, as well as the Tweedie modelling. This new approach is illustrated through simulation and applied to a one-year automobile insurance claims dataset. The hypothesis tests' results, AKaike's Information Criterion (AIC) values and graphical diagnostics all show that the GAMs under both the independent and dependent setting give a better fit than the corresponding previously proposed parametric approach.