The expected discounted penalty at ruin in the Erlang (2) risk process

Li-Juan Sun

Statistics & Probability Letters, 2005, vol. 72, issue 3, 205-217

Abstract: In this paper, under the Erlang (2) risk process, we examine the expected discounted value of a penalty at ruin, which is considered as a function of the initial surplus. We first show that the expected discounted penalty function satisfies an integro-differential equation, and give its initial value, as well as its Laplace transform. We further prove that this function is twice differentiable, and satisfies a defective renewal equation. An explicit expression for the solution of this equation can be derived. The associated compound geometric distribution and "claim size" distribution are also studied.

Keywords: Erlang; (2); risk; process; Expected; discounted; penalty; function; Ruin; probability (search for similar items in EconPapers)
Date: 2005
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Citations: View citations in EconPapers (7)

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