Dividend Maximization Under a Set Ruin Probability Target in the Presence of Proportional and Excess-of-loss Reinsurance

Abstract

We study dividend maximization with set ruin probability targets for an insurance company whose surplus is modelled by a diffusion perturbed classical risk process. The company is permitted to enter into proportional or excess-of-loss reinsurance arrangements. By applying stochastic control theory, we derive Volterra integral equations and solve numerically using block-by-block methods. In each of the models, we have established the optimal barrier to use for paying dividends provided the ruin probability does not exceed a predetermined target. Numerical examples involving the use of both light- and heavy-tailed distributions are given. The results show that ruin probability targets result in an improvement in the optimal barrier to be used for dividend payouts. This is the case for light- and heavy-tailed distributions and applies regardless of the risk model used.