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On the discounted penalty function in a discrete time renewal risk model with general interclaim times. (English) Zbl 1224.91094
A discrete time Sparre Andersen risk model with an arbitrary interclaim times distribution is considered and some general analytic properties of the expected discounted penalty (Gerber-Shiu) function $$\phi_v(u)$$ are explored. It is shown that $$\phi_v(u)$$ satisfies a recursive formula. An explicit expression for $$\phi_v(u)$$ is derived in terms of a compound geometric distribution function for general penalty function. In particular, constant claim amounts and mixed geometric claim amounts are studied.

MSC:
 91B30 Risk theory, insurance (MSC2010) 62P05 Applications of statistics to actuarial sciences and financial mathematics
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