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According to in-depth research, a wide range of problems in applied science involve estimating the probability of compound stochastic sums of heavy-tailed risks over a large threshold. Many researchers have explored this issue from different aspects in recent times. There are two main difficulties here: one is how to deal with the heavy tail of risk, and another is how to handle the dependence of the aggregated processes. Aimed at these two main problems, we investigate the asymptotic properties of the tail of compound stochastic sums of heavy-tailed risks in a general dependence framework, and some approximate bounds and key characteristics related to value-at-risk are also derived. Several practical examples are given to demonstrate the effectiveness of the approximation results. Furthermore, the main results in this paper can be applied to studies of stochastic models in finance and econometrics and studies of dependent netput processes of the M/G/1 queuing systems, etc.

Some Approximate Results of Value-at-Risk for Dependent Compound Stochastic Sums of Heavy-Tailed Risks