Three methods to calculate the probability of ruin

Details

Serval ID
serval:BIB_9B215A737265
Type
Article: article from journal or magazin.
Collection
Publications
Title
Three methods to calculate the probability of ruin
Journal
ASTIN Bulletin
Author(s)
Dufresne, F., Gerber, H.U. 
Publication state
Published
Issued date
1989
Volume
19
Number
1
Pages
71-90
Abstract
The first method, essentmlly due to GOOVAERTS and DE VYLDER, uses the
connection between the probabiliy of ruin and the maximal aggregate loss random
variable, and the fact that the latter has a compound geometric distribution.
For the second method, the claim amount distribution is supposed to be a
combination of exponential or translated exponential distributions. Then the
probability of ruin can be calculated in a transparent fashion; the main problem
is to determine the nontrivial roots of the equation that defines the adjustment
coefficient. For the third method one observes that the probability of ruin is
related to the stationary distribution of a certain associated process. Thus it can
be determined by a single simulation of the latter. For the second and third
methods the assumption of only proper (positive) claims is not needed.
Keywords
Probability of ruin, discretizatlon, combination of exponentials, simulation.
Create date
19/11/2007 11:42
Last modification date
20/08/2019 16:02
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