Asymptotics of Ruin Probabilities for Risk Processes under Optimal Reinsurance and Investment Policies: The Large Claim Case

In a classical risk process reinsurance and investment can be chosen at any time. We find the Lundberg exponent and the Cramér–Lundberg approximation for the ruin probability under the optimal strategy in the case where no exponential moments for the claim size distribution exist. We also show that the optimal strategies converge.