Asymptotic estimations for a nonstandard bidimensional risk model with dependent claims and constant interest force

Source abstract

In this paper we extend the results from Yang and Li(2017), in a non-renewal driven bivariate risk model. Concretely, we are interested in the asymptotic behavior of the joint tail of the discounted aggregate claims over finite and infinite time horizon in a bivariate risk model with two arbitrarily dependent counting processes. We additionally suppose that the sequences of claim-sizes of the two lines of business are independent, but each of them contains weakly dependent terms. In our main results, on finite and on infinite time horizon, we assume two (different) general conditions for the counting processes, that are satisfied by a wide spectrum of processes beyond the renewal ones. In the case of finite horizon we suppose that the claim distributions from the two lines, belong to the subexponential distribution class, while in the case of infinite horizon we restrict ourselves to the consistently varying and positively decreasing distribution class. More explicit asymptotic expressions are derived in the case we are restricted on the regularly varying class for the claim distributions. We note that our results indicate the presence of multivariate non-linear single big jump principle for the discounted aggregate claims.