✦ LIBER ✦

The joint distribution of the time of ruin, the surplus immediately before ruin, and the deficit at ruin

✍ Scribed by Hans U. Gerber; Elias S.W. Shiu

Publisher: Elsevier Science
Year: 1997
Tongue: English
Weight: 366 KB
Volume: 21
Category: Article
ISSN: 0167-6687
DOI: 10.1016/s0167-6687(97)00027-9

No coin nor oath required. For personal study only.

✦ Synopsis

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 Dickson's (I 992) 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.

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