Statistical Estimation of Driving Quality in Car Insurance: Counteraction to Insurance Fraud and the Implementation of Pay-How-You-Drive Approach

This paper adresses the analysis of the application of telematics data in auto insurance in order to counteract insurance fraud and to implement Pay-How-You-Drive approach using statistical methods (logistic regression, k-means and k-nearest neighbors methods, Chow test) and machine learning models (decision trees, algorithms based on gradient boosting). As a result of the study, a clustering model was proposed based on the Chow test for the presence of structural shifts in the variables, which, in combination with dimensionality reduction methods, made it possible to achieve the quality of dividing drivers into "dangerous" and "safe" clusters by their driving style above 0.75 according to the silhouette metric. The problem of driver identification was solved using the algorithm of Extreme Gradient Boosting with the share of correct answers of the classifier over 99%. The results of the study may be useful to insurance companies implementing insurance products based on the use of telematics in their actuarial practice, since the algorithms obtained are of high quality and are able to both identify drivers and separate them according to the degree of risk associated with the quality of their driving.