Joint Modeling of Claim Frequencies and Behavioral Signals in Motor Insurance

Abstract

Telematicsdevices installed in insured vehicles provide actuaries with new risk factors, such as the time of the day, average speeds, and other driving habits. This paper extends the multivariate mixed model describing the joint dynamics of telematics data and claim frequencies proposed by Denuit et al. (2019a) by allowing for signals with various formats, not necessarily integer-valued, and by replacing the estimation procedure with the Expected Conditional Maximization algorithm. A numerical study performed on a database related to Pay-How-You-Drive, or PHYD motor insurance illustrates the relevance of the proposed approach for practice.

Microscopic traffic models, accidents, and insurance losses

“…We refer to Gao et al (2022) for a methodological overview. Verbelen et al (2018), Corradin et al (2021), So et al (2021), and Henckaerts and Antonio (2022) discuss telematics pricing and usage-based auto insurance products.…”

“…(2018), Corradin et al . (2021), So et al . (2021), and Henckaerts and Antonio (2022) discuss telematics pricing and usage-based auto insurance products.…”

Bivariate Poisson Credibility Model and Bonus–Malus Scale for Claim and Near-Claim Events

“…The reason is that GLM/GAM analysis of the scores given random effects in these papers is replaced with GBM in the present study. In principle, it is possible to use GBM in each cycle of the Expected Conditional Maximization (ECM) algorithm proposed by Corradin et al (2022) but this would require considerable computation time. For this rea-son, we adopt here the pragmatic approach of Pechon et al ( 2018) for estimating the parameters entering the bivariate credibility model joining the numbers of claims at fault and near-claim events.…”

“…Dionne and Vanasse (1992) , Pinquet (1998), Gomez-Deniz (2016), Park et al (2018), Cheung et al (2021), Denuit and Lu (2021), Tzougas and Cerchiara (2021) and Verschuren (2022), as well as the references therein. To recognize that telematics data are recorded while the policyholders are driving, exactly as claim experience, Denuit et al (2019) and Corradin et al (2022) proposed to use multivariate credibility models (also called mixed models, in statistics) to capture the joint dynamics of telematics data and claim experience. Past telematics signals are not included in the score like ordinary risk factors but used for premium correction in experience rating.…”

\">i<When theres no November rain>/i<\": developing a parametric insurance for hydroelectric energy generators in Brazil

“…Besides the development of pricing methods for traditional insurance, new types of insurance coverages have emerged recently, along with digitalization and insurtechs, requiring the adaptation of pricing strategies and methods. That is the case, for instance, of cyber insurance, intermittent insurancealso known as pay-as-you-drive (PAYD) when applied in automobile insurance -, and pay-how-you-drive (PHYD)automobile insurance that offers different prices according to the policyholder's driving habits (Arumugam & Bhargavi, 2019;Ayuso et al, 2014;Biener et al, 2015;Braun & Schreiber, 2017;Corradin et al, 2022;Denuit et al, 2019;Dijksterhuis et al, 2015;Eling & Zhu, 2018;Khakifirooz et al, 2021;Malavasi et al, 2021;Reimers & Shiller, 2019;Stoeckli et al, 2018;Tselentis et al, 2018;Volosovych et al, 2021). PAYD and PHYD are usually possible through telematics.…”