Date of Completion

12-7-2016

Embargo Period

12-7-2016

Keywords

time-dependent predictors, fixed target, Generalized Linear Model, Accelerated Failure Time Model, Cumulative Longitudinal Model, Bayesian, Survival Analysis, Generalized Linear Mixed Model

Major Advisor

Lynn Kuo

Associate Advisor

Naitee Ting

Associate Advisor

Manuel A. Nunez

Field of Study

Statistics

Degree

Doctor of Philosophy

Open Access

Open Access

Abstract

The task of predicting the ultimate payment while a claim is open is critical to insurance claim reserving. It faces three main challenges: (a) right censoring in generalized linear models (GLM), (b) predicting an ultimate fixed target with time-dependent predictors, (c) correlated observations in the same subject. We present three methods in addressing these challenges: (1) a series of GLM and accelerated failure time (AFT) models, (2) a series of Bayesian models, (3) the cumulative longitudinal models (CLM) and generalized linear mixed models (GLMM). For each method, I explore the theoretical foundation, apply it on real claim data, and compare the model performance among alternatives. The advantages and limitations of each method are discussed.

Contributions include (a) proving the equivalence in MLE between GLM and AFT based on the gamma distribution and the log link, (b) empirically showing that a linear combination of insignificant predictors could be a significant predictor itself, (c) proposing a new way to generate the joint likelihood for nested observations in CLM. Finally, future areas of research are discussed.

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