Predictive Modeling Applications in Actuarial Science
- Volume 1
- Introduction
- Predictive Modeling Foundations
- Predictive Modeling Methods
- Bayesian and Mixed Modeling
- Longitudinal Modeling
- Volume 2
- Generalized Linear Model
- Extensions of the Generalized Linear Model
- Unsupervised Predictive Modeling Methods
-
Applications on Current Problems in Actuarial Science
- Chapter 8 - The Predictive Distribution of Loss Reserve Estimates over a Finite Time Horizon
- Chapter 9 - Finite Mixture Model and Workers’ Compensation Large-Loss Regression Analysis
- Chapter 10 - A Framework for Managing Claim Escalation Using Predictive Modeling
- Chapter 11 - Predictive Modeling for Usage-Based Auto Insurance
Chapter 9 - Finite Mixture Model and Workers’ Compensation Large-Loss Regression Analysis
Authors
Luyang Fu | Cincinnati Insurance Companies
luyang_fu@Yahoo.com
Xianfang Liu | Cincinnati Insurance Companies
Frank_Liu@cinfin.com
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Actuaries have been studying loss distributions since the emergence of the profession. Numerous studies have found that the widely used distributions, such as lognormal, Pareto, and gamma, do not fit insurance data well. Mixture distributions have gained popularity in recent years because of their flexibility in representing insurance losses from various sizes of claims, especially on the right tail. To incorporate the mixture distributions into the framework of popular generalized linear models (GLMs), the authors propose to use nite mixture models (FMMs) to analyze insurance loss data. The regression approach enhances the traditional whole-book distribution analysis by capturing the impact of individual explanatory variables. FMM improves the standard GLM by addressing distribution-related problems, such as heteroskedasticity, over- and underdispersion, unobserved heterogeneity, and fat tails. A case study with applications on claims triage and on high-deductible pricing using workers’ compensation data illustrates those benefits.