Facing a competitive insurance market, the insurers have to adopt the best marketing strategy to attract the lowest risky agents, (i.e. the good drivers with the lowest probability of accidents), and to retain them within their portfolios of policyholders. Still insurers need to estimate the low risks in the context of asymmetric information. In this paper, we construct an indicator of past claims, which combines the Bonus-Malus coefficient (BM) and the seniority of the driver. This indicator is a better estimate of the past claims than the BM coefficient alone. Since longitudinal data are not available, this indicatoris also used to study the issue of information asymmetry. Using a bivariate logit model to avoid bias and provide robust results, we find that the marginaleffect (+9% on average) of this indicator of past claims, on the actual claims, is more significantthan other exogenous variables. The policyholders with a third-party insurance contract have, on average, a larger probability to incurclaims.