Exact asymptotics of ruin probabilities with linear Hawkes arrivals

Abstract

In this contribution we consider a risk process whose arrivals are driven by a linear marked Hawkes process. Using an appropriate change of measure and a generalized renewal theorem, we are able to derive the exact asymptotics of the process’s ruin probability in the case of light-tailed claims. On the other hand, we can exploit the principle of one large jump to derive the analogous result in the heavy-tailed situation. Furthermore, we derive several intermediate results like the Harris recurrence of the Hawkes intensity process which are of their own interest.