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Risks 2018, 6(3), 83; https://doi.org/10.3390/risks6030083

Bayesian Adjustment for Insurance Misrepresentation in Heavy-Tailed Loss Regression

Division of Statistics, Northern Illinois University, Dekalb 60115, IL, USA
Received: 24 July 2018 / Revised: 9 August 2018 / Accepted: 10 August 2018 / Published: 17 August 2018
(This article belongs to the Special Issue Heavy-Tail Phenomena in Insurance, Finance, and Other Related Fields)
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Abstract

In this paper, we study the problem of misrepresentation under heavy-tailed regression models with the presence of both misrepresented and correctly-measured risk factors. Misrepresentation is a type of fraud when a policy applicant gives a false statement on a risk factor that determines the insurance premium. Under the regression context, we introduce heavy-tailed misrepresentation models based on the lognormal, Weibull and Pareto distributions. The proposed models allow insurance modelers to identify risk characteristics associated with the misrepresentation risk, by imposing a latent logit model on the prevalence of misrepresentation. We prove the theoretical identifiability and implement the models using Bayesian Markov chain Monte Carlo techniques. The model performance is evaluated through both simulated data and real data from the Medical Panel Expenditure Survey. The simulation study confirms the consistency of the Bayesian estimators in large samples, whereas the case study demonstrates the necessity of the proposed models for real applications when the losses exhibit heavy-tailed features. View Full-Text
Keywords: misrepresentation; rate making; predictive analytics; heavy-tailed regression models; Bayesian inference; Markov chain Monte Carlo misrepresentation; rate making; predictive analytics; heavy-tailed regression models; Bayesian inference; Markov chain Monte Carlo
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Xia, M. Bayesian Adjustment for Insurance Misrepresentation in Heavy-Tailed Loss Regression. Risks 2018, 6, 83.

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