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.

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doi.org/10.1017/jpr.2025.6
Journal of Applied Probability
Stochastics

Janssen, A., & Zwart, B. (2025). Infinite-horizon Fuk-Nagaev inequalities. Journal of Applied Probability, 62(3), 1076–1088. doi:10.1017/jpr.2025.6