Predicting Multivariate Insurance Loss Payments Under the Bayesian Copula Framework

• Published in: The Journal of risk and insurance Vol. 80; no. 4; pp. 891 - 919
• Main Authors: Zhang, Yanwei, Dukic, Vanja
• Format: Journal Article
• Language: English
• Published: Malvern Blackwell Publishing Ltd 01.12.2013; Wiley Periodicals, Inc; Blackwell; American Risk and Insurance Association, Inc
• Subjects: Accidents; Actuarial science; Analysis; Automobile insurance; Bayes-Statistik; Bayesian analysis; Bayesian statistical decision theory; Copula functions; Economic aspects; Evaluation; Financial analysis; Generalized linear model; Industry forecasts; Insurance claims; Insurance companies; Insurance industry; Liability (Law); Liability insurance; Loss reserves; Management; Methods; Modeling; Multivariate analysis; Multivariate Verteilung; Parametric models; Predictive modeling; Property & casualty insurance; Property and casualty insurance; Risikomodell; Schadenversicherung; Statistical inference; Trends; Verlustverrechnung; Workers compensation insurance; United States
• ISSN: 0022-4367; 1539-6975
• DOI: 10.1111/j.1539-6975.2012.01480.x

The literature of predicting the outstanding liability for insurance companies has undergone rapid and profound changes in the past three decades, most recently focusing on Bayesian stochastic modeling and multivariate insurance loss payments. In this article, we introduce a novel Bayesian multivariate model based on the use of parametric copula to account for dependencies between various lines of insurance claims. We derive a full Bayesian stochastic simulation algorithm that can estimate parameters in this class of models. We provide an extensive discussion of this modeling framework and give examples that deal with a wide range of topics encountered in the multivariate loss prediction settings.