Frequentist Inference in Insurance Ratemaking Models Adjusting for Misrepresentation

Abstract

In insurance underwriting, misrepresentation represents the type of insurance fraud when an applicant purposely makes a false statement on a risk factor that may lower his or her cost of insurance. Under the insurance ratemaking context, we propose to use the expectation-maximization (EM) algorithm to perform maximum likelihood estimation of the regression effects and the prevalence of misrepresentation for the misrepresentation model proposed by Xia and Gustafson [(2016) The Canadian Journal of Statistics, 44, 198–218]. For applying the EM algorithm, the unobserved status of misrepresentation is treated as a latent variable in the complete-data likelihood function. We derive the iterative formulas for the EM algorithm and obtain the analytical form of the Fisher information matrix for frequentist inference on the parameters of interest for lognormal losses. We implement the algorithm and demonstrate that valid inference can be obtained on the risk effect despite the unobserved status of misrepresentation. Applying the proposed algorithm, we perform a loss severity analysis with the Medical Expenditure Panel Survey data. The analysis reveals not only the potential impact misrepresentation may have on the risk effect but also statistical evidence on the presence of misrepresentation in the self-reported insurance status.

Robust estimates of insurance misrepresentation through kernel quantile regression mixtures

“…Finally, in Section 6.2 the proposed model is applied to study the MEPS data. In line with the results of Akakpo et al (2019), our model suggests a significant percentage of respondents misrepresented on the self‐reported insurance status in 2014, to avoid the potential tax penalty. However, our estimated percentage is substantially lower than that reported in Akakpo et al (2019).…”

“…In line with the results of Akakpo et al (2019), our model suggests a significant percentage of respondents misrepresented on the self‐reported insurance status in 2014, to avoid the potential tax penalty. However, our estimated percentage is substantially lower than that reported in Akakpo et al (2019). This discrepancy may be attributed to the fact that the proposed KQR method could better cope with the nonlinear dependence structure inherent in the MEPS data, and thus leads to a more reliable estimation of the misrepresentation probability.…”

“…To the best of our knowledge, there are only a few existing works on misrepresentation modeling, including Akakpo et al (2019), Xia (2018), Xia and Gustafson (2016, 2018), and Xia et al (2018). In particular, one of the most recent attempts made in Akakpo et al (2019) significantly inspires our undertakings.…”

“…To the best of our knowledge, there are only a few existing works on misrepresentation modeling, including Akakpo et al (2019), Xia (2018), Xia and Gustafson (2016, 2018), and Xia et al (2018). In particular, one of the most recent attempts made in Akakpo et al (2019) significantly inspires our undertakings. In that paper, the authors built on the theoretical groundwork established by Xia and Gustafson (2016) and proposed a mixture of parametric regression to model insurance misrepresentation.…”

“…In that paper, the authors built on the theoretical groundwork established by Xia and Gustafson (2016) and proposed a mixture of parametric regression to model insurance misrepresentation. Before placing the present paper into perspective, the following paragraphs give a coarse overview of the misrepresentation model in Akakpo et al (2019). Some standard notations for describing the misrepresentation problem of interest are needed beforehand.…”