Ruin Probabilities for Risk Processes with Non-Stationary Arrivals and Subexponential Claims

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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.