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Moments of the surplus before ruin and the deficit at ruin in the Erlang(2) risk process. (English) Zbl 1084.60544
Summary: This paper investigates the moments of the surplus before ruin and the deficit at ruin in the Erlang(2) risk process. Using the integro-differential equation that we establish, we obtain some explicit expressions for the moments. Furthermore, when the claim size is exponentially and subexponentially distributed, asymptotic relationships for the moments are derived as the initial capital tends to infinity. Also, we show the joint probability density function of the surplus before ruin and the deficit at ruin.

MSC:
60K05 Renewal theory
60K10 Applications of renewal theory (reliability, demand theory, etc.)
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