Ruin probabilities for risk processes with non-stationary arrivals and subexponential claims

Lingjiong Zhu

Research output: Contribution to journalArticlepeer-review

36 Scopus citations

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 languageEnglish (US)
Pages (from-to)544-550
Number of pages7
JournalInsurance: Mathematics and Economics
Volume53
Issue number3
DOIs
StatePublished - Nov 2013

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.

Copyright:
Copyright 2013 Elsevier B.V., All rights reserved.

Keywords

  • Hawkes processes
  • Non-stationary processes
  • Risk processes
  • Ruin probabilities
  • Self-correcting point processes
  • Shot noise processes
  • Subexponential distributions

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