L undberg Inequality for Ruin Probability

Abstract This article surveys the main results and developments of Lundberg inequality for ruin probability. We briefly describe various insurance risk models in the literature, as well as the Lundberg inequality for ruin probability under these models. Finite time horizon insurance risk model and the effect of the invest income are discussed. We also mention some main results, including the Lundberg type inequality, for the severity of ruin, the distribution of surplus before ruin, and the joint distribution of surplus before and after ruin.