A stochastic comparison of customer classifiers with an application to customer attrition in commercial banking

Abstract

The classification of clients is an essential matter in commercial banking, insurance companies, electrical corporations, communication business, etc. Those companies frequently classify their customers by means of the information provided by the so-called classifier. Motivated by the need to compare systems of classification we introduce a new stochastic order which permits the comparison of classifiers. The stochastic order is analyzed in detail, providing characterizations and properties as well as connections with other stochastic orders and other classification systems. Such an order is applied to compare some classifiers used by a Spanish commercial banking to analyze the key problem of customer churn, obtaining conclusive results by means of real databases. Namely, the optimal classifier among them in the new stochastic order is obtained.

Non-life insurance cancellation: a systematic quantitative literature review

“…The publications selected were analysed according to their methodological approach. Eight papers are theoretical (Larsson and Broström 2019;Brophy 2015;Gallo 2014;Van Gelder et al 2018;Guillenet al 2008;Naujoks et al 2017;Rawson et al 2013;Julie Robson 2015) and 18 are empirical; of the latter, 16 are quantitative (Bolancé et al 2016;Brockett et al 2008;de la Llave et al 2019;Felício and Freire 2016;Frank and Lamiraud 2009;Gamble et al 2009;Guillen et al 2003Guillen et al , 2009Guillén et al 2012;Günther et al 2014;Haugen and Moger 2016;Jeong et al 2018;Lin 2010;López-Díaz et al 2017;Paredes 2018;Staudt and Wagner 2018), one is qualitative (Robson and Sekhon 2011) and one uses a mixed methodology (Dominique-Ferreira 2018). This sample indicates that the study of the cancellation of insurance policies is predominantly conducted through empirical quantitative analysis.…”

“…Regarding the methods of data collection for the empirical research, longitudinal analysis predominates, applied in 11 papers (Bolancé et al 2016;Brockett et al 2008;de la Llave et al 2019;Guillen et al 2003Guillen et al , 2009Guillén et al 2012;Günther et al 2014;Haugen and Moger 2016;Jeong et al 2018;Paredes 2018;Staudt and Wagner 2018), over cross-sectional analysis, used in six papers (Frank and Lamiraud 2009;Gamble et al 2009;Lin 2010;Robson and Sekhon 2011;López-Díaz et al 2017), including the paper that used a mixed qualitative and quantitative methodology (Dominique-Ferreira 2018). In the paper by Felício and Freire (2016), both longitudinal and cross-sectional approaches were applied.…”

“…Considering the statistical techniques applied in the analysis, logistic regressions are predominantly used, employed in six articles (Frank and Lamiraud 2009;Guillen et al 2003Guillen et al , 2009Günther et al 2014;López-Díaz et al 2017;Staudt and Wagner 2018). Brockett et al (2008) and Paredes (2018) used logistic regression and survival analysis.…”

A criterion for the comparison of binary classifiers based on a stochastic dominance with an application to the sale of home insurances

“…Special attention has been focused on this question during the last years (see, for instance, Lloyd (1998), Lee (1999), Hand (2009), Hand and Zhou (2009), Hand (2010), Hand (2012), Hand and Anagnostopoulos (2012), Hand and Anagnostopoulos (2013), Yousef (2013), etc. ) A criterion for the comparison of classifiers based on the theory of stochastic orders was introduced in López- Díaz et al (2017). We describe that procedure briefly, in order to clarify the proposal of the present manuscript.…”

Some Comments on Stochastic Orders and Posets

“…Pre-orders on sets of probabilities are called stochastic orders (see for instance [4], [25] and [29]). Stochastic orders have been successfully applied in areas like medicine, ecology, veterinary science, biology, economics, quality control theory, shape analysis, communications, etc (see for instance [2], [7], [8], [19], [20], [21], [16], [25], [17], [5], [30], [9], etc).…”