An insensitivity property of ladder height distributions

An insensitivity property of ladder height distributions

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Article ID: iaor1994288
Country: Israel
Volume: 29
Issue: 3
Start Page Number: 616
End Page Number: 624
Publication Date: Sep 1992
Journal: Journal of Applied Probability
Authors: ,
Abstract:

This paper considers the undershoot of a general continuous-time risk process with dependent increments under a certain initial level. The increments are given by the locations and amounts of claims which are described by a stationary marked point process. Under a certain balance condition, it is shown that the distribution of the undershoot depends only on the mark distribution and on the intensity of the underlying point process, but not on the form of its distribution. In this way an insensitivity property is extended which has been proved in Björk and Grandell for the ruin probability, i.e. for the probability that after a finite time interval the initial level will be crossed from above.

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