Asymptotic estimates for finite-time ruin probabilities in a generalized dependent bidimensional risk model with CMC simulations

Abstract

<p style='text-indent:20px;'>This paper studies ruin probabilities of a generalized bidimensional risk model with dependent and heavy-tailed claims and additional net loss processes. When the claim sizes have long-tailed and dominated-varying-tailed distributions, precise asymptotic formulae for two kinds of finite-time ruin probabilities are derived, where the two claim-number processes from different lines of business are almost arbitrarily dependent. Under some extra conditions on the independence relation of claim inter-arrival times, the class of the claim-size distributions is extended to the subexponential distribution class. In order to verify the accuracy of the obtained theoretical result, a simulation study is performed via the crude Monte Carlo method.</p>

On the non-closure under convolution for strong subexponential distributions

“…The following dependence structure was introduced in [40] and it was studied in several paper including [54], [40] and [27]. We give this condition of dependence for non-negative random variables and in case these random variables are not bounded from below, we need another condition, as follows.…”