Paulsen, Jostein, On Cramér-like asymptotics for risk processes with stochastic return on investments, Annals of applied probability , 12(4), 2002, pp. 1247-1260
We consider a classical risk process compounded by another independent process. Both of these component processes are assumed to be Lévy processes. We show asymptotically that as initial capital y increases the ruin probability will essentially behave as y.., where . depends on one of the component processes.