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Ruin probability with certain stationary stable claims generated by conservative flows

Part of: Stochastic processes Applications

Published online by Cambridge University Press:  01 July 2016

Uğur Tuncay Alparslan  and
Gennady Samorodnitsky
Uğur Tuncay Alparslan*
Affiliation:
University of Nevada, Reno
Gennady Samorodnitsky*
Affiliation:
Cornell University
*
∗ Postal address: Department of Mathematics and Statistics, University of Nevada, Reno, NV 89557, USA. Email address: [email protected]
∗∗ Postal address: School of Operations Research and Industrial Engineering, Cornell University, Ithaca, NY 14853, USA.
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Abstract

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We study the ruin probability where the claim sizes are modeled by a stationary ergodic symmetric α-stable process. We exploit the flow representation of such processes, and we consider the processes generated by conservative flows. We focus on two classes of conservative α-stable processes (one discrete-time and one continuous-time), and give results for the order of magnitude of the ruin probability as the initial capital goes to infinity. We also prove a solidarity property for null-recurrent Markov chains as an auxiliary result, which might be of independent interest.

Keywords

Ruin probabilitystable processheavy tailergodic theorylong range dependenceconservative flownull-recurrent Markov chainfractional Brownian motion

MSC classification

Primary: 60G52: Stable processes
Secondary: 62P05: Applications to actuarial sciences and financial mathematics
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 39 , Issue 2 , June 2007 , pp. 360 - 384
Copyright
Copyright © Applied Probability Trust 2007 

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