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Infinite-horizon Fuk–Nagaev inequalities

Part of: Limit theorems Mathematical economics

Published online by Cambridge University Press:  16 June 2025

A. J. E. M. Janssen  and
B. Zwart
A. J. E. M. Janssen
Affiliation:
Eindhoven University of Technology
B. Zwart*
Affiliation:
CWI and Eindhoven University of Technology
*
*Postal address: P. O. Box 94079, 1090 GB Amsterdam, The Netherlands. Email: bert.zwart@cwi.nl
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Abstract

We develop explicit bounds for the tail of the distribution of the all-time supremum of a random walk with negative drift, where the increments have a truncated heavy-tailed distribution. As an application, we consider a ruin problem in the presence of reinsurance.

Keywords

Random walkheavy tailsconcentration boundsreinsurance

MSC classification

Primary: 60F10: Large deviations
Secondary: 91B30: Risk theory, insurance
Type
Original Article
Information
Journal of Applied Probability , First View , pp. 1 - 13
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Applied Probability Trust

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