Risk theory for the compound Poisson process that is perturbed by diffusion

Details

Serval ID
serval:BIB_2E54355E2404
Type
Article: article from journal or magazin.
Collection
Publications
Title
Risk theory for the compound Poisson process that is perturbed by diffusion
Journal
Insurance: Mathematics and Economics
Author(s)
Dufresne F., Gerber H. U.
Publication state
Published
Issued date
1991
Volume
10
Number
1
Abstract
The classical model of collective risk theory is extended in that a diffusion process is added to the compound Poisson process. It is shown that the probabilities of ruin (by oscillation or by a claim) satisfy certain defective renewal equations. The convolution formula for the probability of ruin is derived and interpreted in terms of the record highs of the aggregate loss process. If the distribution of the individual claim amounts are combinations of exponentials, the probabilities of ruin can be calculated in a transparent fashion. Finally, the role of the adjustment coefficient (for example, for the asymptotic formulas) is explained.
Keywords
Ruin theory, Risk theory, Renewal equation, Convolution formula, Diffusion, Combinations of exponential claim amounts
Create date
19/11/2007 9:58
Last modification date
20/08/2019 13:12
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