Optimal Claiming Strategies in Bonus Malus Systems and Implied Markov Chains

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.

The paper is now online on http://papers.ssrn.com/id=2790583 and https://hal.archives-ouvertes.fr/hal-01326798.

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,


3 thoughts on “Optimal Claiming Strategies in Bonus Malus Systems and Implied Markov Chains”

  1. Great paper and especially pleased to see it considers different economic utility / behaviours of the drivers.
    Just on the last comment in the paper where you mention that the drivers’ lack of information on \lambda will introduce a bias: the drivers also lack information on the distribution of L, the loss, and quickly comparing figure 5 with 6 I am guessing this may be a greater source of bias? Or am I missing something?
    [And the next question is then if the insurance company should actively share \lambda and L with their customers to encourage different behaviour: would that be value-creating or -destroying in a realistic market?]

    1. no, you’re completely right ! indeed… but my feeling it that usually, a company can a better prediction of \lambda than parameters of L, as well as clients. I would say that distribution of L is more a second order issue…

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