Title of article
The joint distribution of the time of ruin, the surplus immediately before ruin, and the deficit at ruin
Author/Authors
Gerber، نويسنده , , Hans U. and Shiu، نويسنده , , Elias S.W.، نويسنده ,
Issue Information
روزنامه با شماره پیاپی سال 1997
Pages
9
From page
129
To page
137
Abstract
We examine the joint distribution of the time of ruin, the surplus immediately before ruin, and the deficit at ruin. The time of ruin is analyzed in terms of its Laplace transform, which can naturally be interpreted as discounting. We show that, as a function of the initial surplus, the joint density satisfies a certain renewal equation. We generalize Dicksonʹs (1992) formula, which expresses the joint distribution of the surplus immediately before ruin and the deficit at ruin in terms of the probability of ultimate ruin.
Keywords
Lundbergיs fundamental equation , Beekmanיs convolution series , Renewal equation , time of ruin , martingales , Dicksonיs formula , Surplus process , Collective risk theory , Duality , Ruin probability , Deficit at ruin , Laplace transforms , Optional sampling theorem
Journal title
Insurance Mathematics and Economics
Serial Year
1997
Journal title
Insurance Mathematics and Economics
Record number
1541780
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