The Discounted Joint Distribution of the Surplus Prior to Ruin and the Deficit at Ruin in a Sparre Andersen Model

Jiandong Ren

North American Actuarial Journal, 2007, vol. 11, issue 3, 128-136

Abstract: In this article, we consider the risk model with phase-type interclaim times. We first derive a simple matrix-form expression for the discounted joint density of the surplus prior to ruin and the deficit at ruin when the initial surplus is zero. Then we express the discounted joint density in terms of certain expected discounted penalty functions when the initial surplus is greater than zero. This result generalizes that in Gerber and Shiu (1997).

Date: 2007
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DOI: 10.1080/10920277.2007.10597471

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