Ruin problem and how fast stochastic processes

The recent increasing interplay between actuarial and financial mathematics has led to a surge in risk theoretic modeling. Especially actuarial ruin models under fairly general conditions on the underlying risk process have become a focus of attention. Motivated by applications such as the modeling of operational risk losses in financial risk management, we investigate the stability of classical asymptotic ruin estimates when claims are heavy, and this under variability of the claim intensity process. Various examples are discussed.