Asymptotics for ruin probabilities in a bidimensional discrete-time risk model with dependent and consistently varying tailed net losses

Abstract

Consider an insurer who operates two lines of businesses and hence receives two types of insurance net losses. In the bidimensional discrete-time risk model with a constant interest rate, the net loss vectors from the two business lines form a sequence of independent and identically distributed real-valued random vectors. We propose a bidimensional extended regularly varying structure in terms of survival copulas to model the dependence between the two components of each net loss vector, which includes not only asymptotic independence but also asymptotic dependence. Under the framework of consistent variation, we obtain several (uniformly) asymptotic formulas for various ruin probabilities. In particular, the investigation of random-time ruin probabilities unifies and extends the results on both finite-time and infinite-time ruin probabilities. Some numerical studies are also performed to check the accuracy of our obtained asymptotic results.