Ruin Probabilities for Risk Processes with Non-Stationary Arrivals and Subexponential Claims
By Lingjiong Zhu. 2013
64 citations recorded by the source corpus.
In this paper, we obtain the finite-horizon and infinite-horizon ruin probability asymptotics for risk processes with claims of subexponential tails for non-stationary arrival processes that satisfy a large deviation principle. As a result, the arrival process can be dependent, non-stationary and non-renewal. We give three examples of non-stationary and non-renewal point processes: Hawkes process, Cox process with shot noise intensity and self-correcting point process. We also show some aggregate claims results for these three examples.
Subfields: Applied Mathematics, Artificial Intelligence, Management Science and Operations Research
View Paper: https://www.semanticscholar.org/paper/b3a02f61aa881a5d520a78628a0fa37727521b91
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Applied Mathematics
In Artificial Intelligence
In Management Science and Operations Research
Citations in the corpus
- Limit Theorems for Marked Hawkes Processes with Application to a Risk Model (2012, methodology): “(1.8) Moderate deviation principle for linear Hawkes processes is obtained in Zhu [16], which fills in the gap between central limit theorem and large deviation principle.”
- Large deviations for Markovian nonlinear Hawkes processes (2011, background): “s and studied the asymptotic behavior of infinite and finite horizon ruin probabilities under light-tailed conditions on the claims. The corresponding result for heavy-tailed claims was obtained by Zhu [27]. 4 L. ZHU In this paper,we are interested in Hawkes processeswith general nonlinear λ(·). If λ(”