The optimal claiming strategies in a Bonus-Malus System and the monotony property

Yaniv Zaks

Scandinavian Actuarial Journal, 2008, vol. 2008, issue 1, 34-40

Abstract: In the classical Bonus-Malus System (BMS) there are several premium levels, e.g., M. A premium level i consists of a premium (πi) and a deductible (di). In this paper, we consider the expected cost for a horizon of n periods of a policyholder in level i. This expectation is denoted by En(i). When damage of size x occurs, the policyholder should decide whether or not to claim. The minimum damage for which the policyholder will claim should be the solution of . We will show that En−1(i−1) − En−1(i+1), hence x=di+En−1(i+1) ≤ En−1(i−1), is a valid solution.

Date: 2008
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DOI: 10.1080/03461230701722869

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