Risk processes perturbed by α-stable Lévy motion

Hansjörg Furrer

93 citations0/0 files storedScandinavian Actuarial Journal

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Probability and Risk Models Probability and Statistical Research Stochastic processes and financial applications

Abstract

The classical model of collective risk theory is extended in that an α-stable Levy motion is added to the compound Poisson process. The convolution formula for the probability of ruin is derived. We then investigate the asymptotic behaviour of the ruin probability as the initial capital becomes large.

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References

1994Modelling of extremal events in insurance and finance 1991Aspects of Risk Theory 1997Stable Non-Gaussian Random ProcessesGennady Samorodnitsky and Murad S. Taqqu Chapman and Hall, 1994 1979Subexponentiality and infinite divisibility 1991Risk theory for the compound Poisson process that is perturbed by diffusion 1970An extension of the renewal equation and its application in the collective theory of risk 1964The First Passage Time of a Level and the Behavior at Infinity for a Class of Processes with Independent Increments

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