An application of two-stage quantile regression to insurance ratemaking



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Heras Martínez, Antonio José and Moreno, Ignacio and Vilar Zanón, José Luis (2018) An application of two-stage quantile regression to insurance ratemaking. Scandinavian Actuarial Journal, 2018 (9). pp. 753-769. ISSN 0346-1238

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Two-part models based on generalized linear models are widely used in insurance rate-making for predicting the expected loss. This paper explores an alternative method based on quantile regression which provides more information about the loss distribution and can be also used for insurance underwriting. Quantile regression allows estimating the aggregate claim cost quantiles of a policy given a number of covariates. To do so, a first stage is required, which involves fitting a logistic regression to estimate, for every policy, the probability of submitting at least one claim. The proposed methodology is illustrated using a portfolio of car insurance policies. This application shows that the results of the quantile regression are highly dependent on the claim probability estimates. The paper also examines an application of quantile regression to premium safety loading calculation, the so-called Quantile Premium Principle (QPP). We propose a premium calculation based on quantile regression which inherits the good properties of the quantiles. Using the same insurance portfolio data-set, we find that the QPP captures the riskiness of the policies better than the expected value premium principle.

Item Type:Article
Uncontrolled Keywords:Aggregate claims model; Quantile regression; Insurance rate making; Insurance underwriting; Premium risk loading
Subjects:Social sciences > Economics > Insurance
ID Code:60265
Deposited On:29 Apr 2020 12:12
Last Modified:09 Jun 2020 21:10

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