Comment on the work of Zhang et al. (2017, Journal of Inequalities and Applications)

Abstract

Abstract In a recent work by Zhang et al. (J. Inequal. Appl. 2017:82, 2017) the authors studied large deviations of the aggregate amount of claims in a size-dependent renewal risk model. They claimed that they obtained a precise large-deviation formula for the case with subexponential claims and with arbitrary dependence between each claim size and its waiting time. In this short note, we point out that their main result is unfortunately not correct in general.

Keywords

• Aggregate amount of claims
• Precise large deviations
• Subexponential class
• Dependence
• Renewal counting process
• Counterexample