It is proved that the optimal decision rule to claim or not to claim for damage is of the form: ‘to claim for damage only if its amount exceeds a certain limit’. Optimal critical claim sizes are derived, and a sensitivity analysis is given with respect to changes in (the parameters of) the distributions of the number of claims and the claim size.

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Insurance: Mathematics and Economics
Erasmus School of Economics

Dellaert, N.P, Frenk, J.B.G, & Kouwenhoven, A. (1990). Optimal claim behaviour for third-party liability insurances or to claim or not to claim: that is the question. Insurance: Mathematics and Economics, 9(1), 59–76. doi:10.1016/0167-6687(90)90016-7