Abstract
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.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 544-550 |
| Number of pages | 7 |
| Journal | Insurance: Mathematics and Economics |
| Volume | 53 |
| Issue number | 3 |
| DOIs | |
| State | Published - Nov 2013 |
| Externally published | Yes |
Bibliographical note
Funding 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.
Keywords
- Hawkes processes
- Non-stationary processes
- Risk processes
- Ruin probabilities
- Self-correcting point processes
- Shot noise processes
- Subexponential distributions