Asymptotic analysis of the ruin with stationary stable steps generated by dissipative flows

Ugur Tuncay Alparslan and Gennady Samorodnitsky

Scandinavian Actuarial Journal, 2007, vol. 2007, issue 3, 180-201

Abstract: We study the exceedance probability of a high threshold (ruin probability) for a random walk with a negative linear drift, where the steps of the walk (claim sizes) constitute a stationary ergodic symmetric α-stable process. We casually use the language of insurance, although this is a popular problem in many other fields of applied probability as well. We refer to ergodic theory to split the step process into two independent processes. We focus on the processes generated by dissipative flows, which are known to have a mixed moving average representation, and we restrict our attention to regular moving averages with non-negative kernels. We give results for the order of magnitude of the exceedance probability as the threshold goes to infinity in the cases of discrete-time and continuous-time claim processes.

Date: 2007
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DOI: 10.1080/03461230701485681

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