Second order corrections for the limits of normalized ruin times in the presence of heavy tails

TL;DR

This paper analyzes the finite time ruin probability in a risk model with heavy-tailed claims, deriving convergence rates when claims have finite second moments, extending previous asymptotic results.

Contribution

It provides the rate of convergence for ruin probabilities in heavy-tailed claim models with finite second moments, refining existing asymptotic formulas.

Findings

Derived convergence rates for ruin probabilities

Extended asymptotic results to finite second moment claims

Improved understanding of ruin probabilities in heavy-tailed models

Abstract

In this paper we consider a compound Poisson risk model with regularly varying claim sizes. For this model in [1] an asymptotic formula for the finite time ruin probability is provided when the time is scaled by the mean excess function. In this paper we derive the rate of convergence for this finite time ruin probability when the claims have a finite second moment. [1] S. Asmussen and C. Kl\"uppelberg. Large deviations results for subexponential tails, with applications to insurance risk. Stochastic Process. Appl., 64(1):103-125, 1996.