The Annals of Probability
- Ann. Probab.
- Volume 28, Number 4 (2000), 1814-1851.
Ruin probability with claims modeled by a stationary ergodic stable process
For a random walk with negative drift we study the exceedance probability (ruin probability) of a high threshold. The steps of this walk (claim sizes) constitute a stationary ergodic stable process. We study how ruin occurs in this situation and evaluate the asymptotic behavior of the ruin probability for a large variety of stationary ergodic stable processes. Our findings show that the order of magnitude of the ruin probability varies significantly from one model to another. In particular, ruin becomes much more likely when the claim sizes exhibit long-range dependence. The proofs exploit large deviation techniques for sums of dependent stable random variables and the series representation of a stable process as a function of a Poisson process.
Ann. Probab., Volume 28, Number 4 (2000), 1814-1851.
First available in Project Euclid: 18 April 2002
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60E07: Infinitely divisible distributions; stable distributions
Secondary: 60G10: Stationary processes 60K30
Mikosch, Thomas; Samorodnitsky, Gennady. Ruin probability with claims modeled by a stationary ergodic stable process. Ann. Probab. 28 (2000), no. 4, 1814--1851. doi:10.1214/aop/1019160509. https://projecteuclid.org/euclid.aop/1019160509