Bonus systems in an open portfolio. (English) Zbl 1055.91021

Summary: We study bonus systems in an open portfolio, i.e. we consider that a policyholder can transfer his policy to a different insurance company at any time. We make use of inhomogeneous Markov chains to model the system and show, under reasonable assumptions, that the stationary distribution is independent of the market shares, and is easily calculated.


91B28 Finance etc. (MSC2000)
91B30 Risk theory, insurance (MSC2010)
62P05 Applications of statistics to actuarial sciences and financial mathematics
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[1] Borgan, O., Hoem, J., Norberg, R., 1981. A nonasymptotic criterion for the evaluation of automobile bonus systems. Scandinavian Actuarial Journal, 92-107. · Zbl 0476.62080
[2] Cox, D., Miller, H., 1965. The Theory of Stochastic Processes. Chapman & Hall, London. · Zbl 0149.12902
[3] Gilde, V., Sundt, B., 1989. On bonus systems with credibility scales. Scandinavian Actuarial Journal, 13-22. · Zbl 0682.62085
[4] Lemaire, J., 1995. Bonus-Malus Systems in Automobile Insurance. Kluwer Academic Publishers, Boston.
[5] Loimaranta, K., Some asymptotic properties of bonus systems, ASTIN bulletin, 6, 233-245, (1972)
[6] Norberg, R., 1976. A credibility theory for automobile bonus systems. Scandinavian Acturial Journal, 92-107. · Zbl 0337.62071
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