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

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 no...

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Bibliographic Details
Published in:Insurance, mathematics & economics mathematics & economics, 2013-11, Vol.53 (3), p.544-550
Main Author: Zhu, Lingjiong
Format: Article
Language:English
Subjects:
Asymptotic methods
Economic theory
Hawkes processes
Insurance claims
Non-stationary processes
Probability
Risk assessment
Risk processes
Risk theory
Ruin probabilities
Self-correcting point processes
Shot noise processes
Stationarity
Studies
Subexponential distributions
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Summary: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. •Asymptotic ruin probabilities for risk processes with subexponential claims.•Some aggregate claims asymptotics are also studied.•Arrival process can be non-stationary and non-renewal.•The key assumption is arrival process satisfies a large deviation principle.•We apply our results to three examples of arrival processes.
ISSN:0167-6687
1873-5959
DOI:10.1016/j.insmatheco.2013.08.008