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A note on a generalized discounted penalty function in a Sparre Andersen risk model perturbed by diffusion. (English) Zbl 1420.91139

Summary: We consider a Sparre Andersen risk model perturbed by diffusion where the interclaim times are generalized \(\operatorname{Erlang}(n)\) distribution. Generalized discounted penalty functions incorporating the maximum surplus before ruin are studied. We derive the integrodifferential equations and give the solutions for the generalized discounted penalty functions.

MSC:

91B30 Risk theory, insurance (MSC2010)
60K10 Applications of renewal theory (reliability, demand theory, etc.)
45J05 Integro-ordinary differential equations

References:

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