With Arthur David and Romuald Elie, we just wrote a short paper on bonus malus, and optimal strategies to claim a loss (or not)
In this paper, we investigate the impact of the claim reporting strategy of drivers, within a bonus malus system. We exhibit the induced modification of the corresponding class level transition matrix and derive the optimal reporting strategy for rational drivers. The hunger for bonuses induces optimal thresholds under which, drivers do not claim their losses. A numerical algorithm is provided for computing such thresholds and realistic numerical applications are discussed.
Note that we do not discuss here legal issues here (in some contracts, it is compulsory to claim all losses, even small ones), but economic incentives and mathematical issues. Some popular journals in France did mention that issue, of non claims small losses (see http://leparticulier.fr/) but in those standard computations (see below), it is based on some naive model that we improve in our paper,