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On the distribution of the claim causing ruin. (English) Zbl 0783.62083
Summary: We extend the work of F. Dufresne and H. U. Gerber [ibid. 7, No 3, 193-199 (1988; Zbl 0674.62072)] by developing expressions for the distribution function of the claim causing ruin in the classical compound Poisson process. We consider the special case when the initial surplus is zero, as well as illustrating results when the initial surplus is positive. We also consider a discrete time risk model and show how the distribution can be calculated by a recursive method.

MSC:
62P05 Applications of statistics to actuarial sciences and financial mathematics
62E15 Exact distribution theory in statistics
62E20 Asymptotic distribution theory in statistics
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