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Centeno, Maria de Lourdes; Andrade e Silva, João Manuel

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

Insur. Math. Econ. 28, No. 3, 341-350 (2001).
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.

Cited in 1 Review
Cited in 3 Documents

MSC:

91B28 Finance etc. (MSC2000)
91B30 Risk theory, insurance (MSC2010)
62P05 Applications of statistics to actuarial sciences and financial mathematics

Keywords:

Markov chains; Stationary distribution; Closed model
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\textit{M. de L. Centeno} and \textit{J. M. Andrade e Silva}, Insur. Math. Econ. 28, No. 3, 341--350 (2001; Zbl 1055.91021)
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References:

[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.