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 densit
The surpluses immediately before and at ruin, and the amount of the claim causing ruin
✍ Scribed by François Dufresne; Hans U. Gerber
- Book ID
- 107918863
- Publisher
- Elsevier Science
- Year
- 1988
- Tongue
- English
- Weight
- 374 KB
- Volume
- 7
- Category
- Article
- ISSN
- 0167-6687
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Collective risk model with a special emphasize on non-Poissonian claims' arrival processes is considered. Exact and approximate techniques for the calculation of the probabilities of ruin are examined. Simulation going back to the importance sampling is applied to two particular cases of non-Poisson
We obtain explicit expressions for the distribution of surplus immediately before and after ruin which allow for simple derivation of bounds as well as simple evaluation for certain choices of the claim size distribution. We then use these expressions to construct Tijms-type approximations which are