Journal article
The joint distribution of the time of ruin, the surplus immediately before ruin, and the deficit at ruin
Insurance, mathematics & economics, Vol.21(2), pp.129-137
1997
DOI: 10.1016/S0167-6687(97)00027-9
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 Dickson's (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.
Details
- Title: Subtitle
- The joint distribution of the time of ruin, the surplus immediately before ruin, and the deficit at ruin
- Creators
- Hans U Gerber - Ecole des hautes études commerciales, Université de Lausanne, CH-1015 Lausanne, SwitzerlandElias S.W Shiu - Department of Statistics and Actuarial Science, The University of Iowa, Iowa City, Iowa 52242, USA
- Resource Type
- Journal article
- Publication Details
- Insurance, mathematics & economics, Vol.21(2), pp.129-137
- Publisher
- Elsevier B.V
- DOI
- 10.1016/S0167-6687(97)00027-9
- ISSN
- 0167-6687
- eISSN
- 1873-5959
- Language
- English
- Date published
- 1997
- Academic Unit
- Statistics and Actuarial Science
- Record Identifier
- 9983985837602771
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