Abstract
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.
Highlights
A wide range of problems in applied science involve estimating the probability of compound stochastic sums of heavy-tailed risks over a large threshold
The advanced measurement approach (AMA) allows banks to develop their own model for assessing the regulatory capital that covers their yearly operational risk exposure within a confidence interval of 99.9%
THE STOCHASTIC MODEL We first introduce the specific model under the framework of loss distribution approach (LDA) that can be depicted by the ‘loss frequency’ and ‘loss severity’
Summary
A wide range of problems in applied science involve estimating the probability of compound stochastic sums of heavy-tailed risks over a large threshold. For more details on this issue, we refer the interested readers to Haubenstock and Hardin [13], Embrechts et al [14], [15], Chavez-Demoulin et al [16], Degen et al [17], Valle et al [8], Bocker et al [18], Biagini et al [19], Nash [20] and Panjer [21] As is known, another main problem apart from the lack of loss data is establishing an accurate understanding of the degrees of dependence among losses in various units of measures and implementing it in practice.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
