Asymptotic ruin probability of a renewal risk model with dependent by-claims and stochastic returns

Consider a nonstandard renewal risk model, in which every main claim induces a delayed by-claim. Suppose that the surplus is invested to a portfolio of one risk-free asset and one risky asset, and the main claim sizes with by-claim sizes form a sequence of pairwise quasi-asymptotically independent random variables with dominatedly varying tails. Under this setting, asymptotic behavior of the ruin probability of this renewal risk model is investigated, by establishing a weakly asymptotic formula, as the initial surplus tends to infinity. Some numerical results are also presented to illustrate the accuracy of our asymptotic formulae.