On the Gerber-Shiu discounted penalty function in the Sparre Andersen model with an arbitrary interclaim time distribution. (English) Zbl 1152.91591

Summary: We consider the Sparre Andersen risk model with an arbitrary interclaim time distribution and a fairly general class of distributions for the claim sizes. Via a two-step procedure which involves a combination of a probabilitic and an analytic argument, an explicit expression is derived for the Gerber-Shiu discounted penalty function, subject to some restrictions on its form. A special case of Sparre Andersen risk models is then further analyzed, whereby the claim sizes’ distribution is assumed to be a mixture of exponentials. Finally, a numerical example follows to determine the impact on various ruin related quantities of assuming a heavy-tail distribution for the interclaim times.


91B30 Risk theory, insurance (MSC2010)
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