Moments of the Surplus before Ruin and the Deficit at Ruin in the Erlang(2) Risk Process
نویسندگان
چکیده
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.
منابع مشابه
The moments of the time of ruin , the surplus before ruin , and the deficit at ruin
In this paper we extend the results in Lin and Willmot (1999 Insurance: Mathematics and Economics 25, 63–84) to properties related to the joint and marginal moments of the time of ruin, the surplus before the time of ruin, and the deficit at the time of ruin. We use an approach developed in Lin and Willmot (1999), under which the solution to a defective renewal equation is expressed in terms of...
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