Bivariate regular variation among randomly weighted sums in general insurance

Abstract

The tail behavior of randomly weighted sums has become an increasingly interesting topic in applied probability and this study has played an important role in a few problems in insurance, finance, and risk management. In this paper, we extend the study to the case of non-standard bivariate regular variation and, as applications, we interpret the study in terms of bivariate processes of aggregate claims (without interest rate, with a constant force of interest, or with stochastic investment returns).