Maximum Likelihood Approaches to Misrepresentation Models in GLM ratemaking: Model Comparisons

This paper proposes maximum likelihood inference for predictive analytics models of misrepresentation in insurance underwriting. The models allow for multiple risk factors in both the ratemaking models and latent models on misrepresentation. Such latent variable approach enables learning of misrepresentation risk at the policy level without requiring labelled fraud data. We develop expectation maximization algorithms for maximum likelihood estimation under frequency and severity models including lognormal, gamma, Poisson and negative binomial models incorporating misrepresentation. Statistical techniques are proposed to derive standard errors for assessing uncertainty in parameter estimation. Simulation studies are performed to evaluate model estimation, demonstrating the importance of misrepresentation modeling and the advantage of maximum likelihood approaches over Bayesian methods in computational speed. Using the Medical Expenditure Panel Survey data, we perform model comparisons of various frequency and severity models on healthcare utilization and expenditures to assess misrepresentation on the uninsured status. For predictive analytics purposes, we evaluate in-sample and out-of-sample prediction via a variety of methods including those typically adopted in ratemaking.