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A generalized penalty function in Sparre Andersen risk models with surplus-dependent premium. (English) Zbl 1229.91157
The paper focuses on the surplus process of an insurance company, which is modeled as a generalized Sparre Andersen risk model with surplus-dependent premium rate. This assumption allows to obtain a twofold goal: maintaining a competitive level of premiums in case of higher surplus, as well as charging prudential higher premiums in case of insufficient funds.
Firstly, the generalized Gerber-Shiu function is derived by means of a transition function which is independent of the penalty function. Furthermore, properties of this last function are obtained under the assumption of a constant premium, or in the case of a threshold dividend strategy, or considering credit interest.
Some extensions are discussed within an absolute ruin model with debit interest.

MSC:
91B30 Risk theory, insurance (MSC2010)
91B70 Stochastic models in economics
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