  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.
