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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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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description 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.
doi_str_mv 10.1016/j.insmatheco.2013.08.008
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source International Bibliography of the Social Sciences (IBSS); Elsevier SD Backfile Mathematics; ScienceDirect Journals; Elsevier SD Backfile Economics
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
title Ruin probabilities for risk processes with non-stationary arrivals and subexponential claims
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