Geodesic
``Bonus hunger" behavior in the alternative bonus–malus system
Proceedings of the Yerevan State University. Physical and mathematical sciences, Tome 51 (2017) no. 2, pp. 146-150.

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In this article the "bonus hunger" behavior for the Alternative bonus–malus system (BMS) is discussed. The Alternative BMS is a model, where the next premium is the combination of the previous premium and the aggregate claim amount. The key characteristics for the comparison are the discounted premium reduction for some time horizon and the entire claim amount. Existence of the steady state for the BMS discussed in this paper was proved and the probability of claiming for the general model and for its steady state was found out.
Keywords: hunger for bonus, bonus–malus system.
Mots-clés : martingale 
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A. G. Gulyan. ``Bonus hunger" behavior in the alternative bonus–malus system. Proceedings of the Yerevan State University. Physical and mathematical sciences, Tome 51 (2017) no. 2, pp. 146-150. http://geodesic.mathdoc.fr/item/UZERU_2017_51_2_a1/

[111] N.P. Dellaert, J.B.G Frenk., A. Kouwenhoven, “Optimal Claim Behaviour for Third-Party Liability Insurances or to Claim or not to Claim: that is the Question”, Insurance: Mathematics and Economics, 1990, no. 9, 59–76 | DOI | MR | Zbl

[112] J. Lemaire, “Driver Versus Company, Optimal Behaviour of the Policy Holder.”, Scandinavian Actuarial Journal, 1976, no. 59, 209–219 | DOI | Zbl

[113] A. Kozubik, “Bonus–Malus Systems as Markov Process and Hungry for Bonus”, J. of Information, Control and Management Systems, 4:1 (2006,), 9–17

[114] A.G. Gulyan, “An Alternative Model for Bonus–Malus System”, Proceedings of the Yerevan State University. Physical and Mathematical Sciences, 2015, no. 1, 15–19 | Zbl

[115] A.N. Shiryaev, Probability, v. 1, MCCME, M., 2004 (in Russian) | MR