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A risk model with varying premiums: its risk management implications. (English) Zbl 1308.91089
Summary: In this paper, we consider a risk model which allows the insurer to partially reflect the recent claim experience in the determination of the next period’s premium rate. In a ruin context, similar mechanisms to the one proposed in this paper have been studied by, e.g., C. Tsai and G. Parker [“Ruin probabilities: classical versus credibility”, in: NTU international conference on finance (2004)], L. B. Afonso et al. [Astin Bull. 39, No. 1, 117–136 (2009; Zbl 1203.91108)] and S. Loisel and J. Trufin [“Ultimate ruin probability in discrete time with Bühlmann credibility premium adjustments”, Bull. Français d’Actuariat (2013), https://hal.archives-ouvertes.fr/hal-00426790]. In our proposed risk model, we assume that the effective premium rate is determined based on the surplus increments between successive random review times. When review times are distributed as a combination of exponentials and claim arrivals follow a compound Poisson process, we derive a matrix-form defective renewal equation for the Gerber-Shiu function, and provide an explicit expression for the discounted joint density of the surplus prior to ruin and the deficit at ruin. Numerical examples are later considered to numerically evaluate certain ruin-related quantities. A comparison with their counterparts in a constant premium rate model is also presented.

MSC:
91B30 Risk theory, insurance (MSC2010)
60K10 Applications of renewal theory (reliability, demand theory, etc.)
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