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Infinite-horizon Fuk-Nagaev inequalities

A. J. E. M. Janssen, B. Zwart

Abstract

We develop explicit bounds for the tail of the distribution for 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 re-insurance.

Infinite-horizon Fuk-Nagaev inequalities

Abstract

We develop explicit bounds for the tail of the distribution for 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 re-insurance.
Paper Structure (5 sections, 3 theorems, 77 equations, 2 figures)

This paper contains 5 sections, 3 theorems, 77 equations, 2 figures.

Table of Contents

  1. Introduction and main results
  2. Proof of Theorem \ref{['thm-main']}
  3. Proof of Theorem \ref{['thm-main2']}
  4. Application to a re-insurance risk model
  5. Bounding Taylor approximation errors

Key Result

Theorem 1.1

There exists a $y_\beta<\infty$ such that

Figures (2)

  • Figure 1: $ME_\delta$, $UE_\delta$, $1/(1+\delta/2)$ as function of $\delta \in (0,2)$.
  • Figure 2: $MG_\delta$, $UG_\delta$, $1/\delta$ as function of $\delta \in (1,2)$.

Theorems & Definitions (3)

  • Theorem 1.1
  • Theorem 1.2
  • Proposition 4.1