Abstract
We find sharp asymptotics of the probability that the trajectory of a compound renewal process crosses (or does not cross) an arbitrary remote boundary. In particular, some limit theorems are obtained for the distribution of the maximum of the process in the domain of large deviations. We also give some applications to the classical ruin probability problem in insurance theory.
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Russian Text © The Author(s), 2020, published in Sibirskii Matematicheskii Zhurnal, 2020, Vol. 61, No. 1, pp. 29–59.
The author was partially supported by the Program of Basic Scientific Research of the Siberian Branch of the Russian Academy of Sciences (Grant No. I.1.3, Project 0314—2016—0008) as well as funded by the Russian Foundation for Basic Research (Grant 18—01—00101a).
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Borovkov, A.A. Boundary Crossing Problems for Compound Renewal Processes. Sib Math J 61, 21–46 (2020). https://doi.org/10.1134/S0037446620010036
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DOI: https://doi.org/10.1134/S0037446620010036