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Perturbed Risk Processes: a Review

By Hanspeter and Schmidli
Research Reports
No. 407, September 1999
To a risk model an independent perturbation process is added. If the perturbation process is Brownian motion, Lundberg inequalities and Cramér-Lundberg approximations can be proved. Also the asymptotic behaviour of the ruin probability in the case of heavy claims can be obtained. If, the perturbation is a Lévy process, ladder epochs and ladder heights can be defined. In the stationary case, the distribution of the ladder height are obtained. 1991 Mathematical Subject Classification: Primary 60K30; Secondary 60G44, 60J30, &0G10 Key words: Perturbed risk model, ruin probability, Lévy process, Brownian motion, Lévy motion, compound Poisson process, asymptotics
Theory of Stochastic Processes 5 (1999), 145-165
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