Bayesian Adjustment for Insurance Misrepresentation in Heavy-Tailed Loss Regression

Michelle Xia
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Michelle Xia: Division of Statistics, Northern Illinois University, Dekalb 60115, IL, USA

Risks, 2018, vol. 6, issue 3, 1-16

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.

Keywords: misrepresentation; rate making; predictive analytics; heavy-tailed regression models; Bayesian inference; Markov chain Monte Carlo (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:gam:jrisks:v:6:y:2018:i:3:p:83-:d:164344

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