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Risk processes with non-stationary Hawkes claims arrivals. (English) Zbl 1231.91239
Summary: We consider risk processes with non-stationary Hawkes claims arrivals, and we study the asymptotic behavior of infinite and finite horizon ruin probabilities under light-tailed conditions on the claims. Moreover, we provide asymptotically efficient simulation laws for ruin probabilities and we give numerical illustrations of the theoretical results.

MSC:
91B30 Risk theory, insurance (MSC2010)
60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)
65C05 Monte Carlo methods
60K10 Applications of renewal theory (reliability, demand theory, etc.)
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