Ruin probabilities with pairwise quasi-asymptotically independent and dominatedly-varying tailed claims

Abstract

This paper considers the nonstandard renewal risk model in which a part of surplus is invested into a Black-Scholes market whose price process is modelled by a geometric Brownian motion, claim sizes form a sequence of not necessarily identically distributed and pairwise quasi-asymptotically independent random variables with dominatedly-varying tails. The authors obtain a weakly asymptotic formula for the finite-time and infinite-time ruin probabilities. In particular, if the claims are identically distributed and consistently-varying tailed, then an asymptotic formula is presented.