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According to the editorial rules of treating discussion situations in the ASTIN Bulletin the paper by J. Lemaire & H. Zi being somewhat a discussion on Holtan's paper was sent to the author of the original paper, who was given the opportunity to make an additional comment. The editors then received the following note by Jon Holtan:
In this note I want to give some general comments on the papers by Lemaire & Zi (1994) and Holtan (1994).
Interpret henceforth a bonus-malus (BM) principle as consisting of two basic components:
(a) The BM design.
(b) The BM tariff parameters.
Traditional actuarial literature has basically been preoccupied with component (b). Or more precisely, the tariff parameters of an initial accepted BM design have usually been mathematically optimalized within different criteria of succes like e.g. high efficiency and financial balance. In my opinion, however, this strategy seems to be too narrow if the aim is to construct a BM principle which is totally optimalized in favour of both the insurer and the insured. In our strive for maximizing BM advantages and minimizing BM disadvantages, actuarial BM research should instead simultaneously focus on both components (a) and (b). The construction of the High-Deductible System (HDS) in Holtan (1994) is an example of this strategy. However, as pointed out in Lemaire & Zi (1994) (see Section 1 and 4) and Holtan (1994) (see Section 3, 5 and 6), a HDS compared with existing BM systems both eliminates and generates important disadvantages which are linked to component (a). Based on some mathematical model assumptions, Lemaire & Zi moreover concludes (see Section 3 and 5) that this two-sided conclusion is in principle also valid within some mathematical criteria of success linked to component (b). These complex, and perhaps confusing, conclusions make it difficult for us to decide whether to prefer the existing BM systems or the HDS. However, the solution to this problem of decision seems to be naturally dependent on some strategic questions like: What kind of BM advantages and what kind of BM disadvantages will be the most important to focus on in the future automobile insurance market?
