Investigation a Dependent Generalized Compound Renewal Risk Process Involving the Uniformly Bounded Copula Function

In this paper, we investigate the ruin probabilities in a generalized compound renewal risk process based on the claim amounts with dependence structures involving the uniformly bounded copula function. Suppose that the claim amounts are identically distributed having a subexponential class of distributions independent of inter-arrival times. For this dependent generalized risk model, we derive the asymptotic behavior of the finite time ruin probability applying the dominated convergence theorem and mathematical induction. Moreover, we study the asymptotic behavior of the finite time ruin probability for degenerated claim numbers of risk model. Finally, two numerical examples along with some simulation studies for dependent claim amounts with Clayton copula are presented to check the accuracy of the asymptotic results.