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.
Bibliographical noteFunding Information:
The author is supported by NSF grant DMS-0904701 , DARPA grant and MacCracken Fellowship at New York University. The author is very grateful to an anonymous referee for the helpful comments and suggestions.
Copyright 2013 Elsevier B.V., All rights reserved.
- Hawkes processes
- Non-stationary processes
- Risk processes
- Ruin probabilities
- Self-correcting point processes
- Shot noise processes
- Subexponential distributions