Optimal Reinsurance Strategy with Bivariate Pareto Risks

Abstract

In an insurance, one is often concerned with risks and extreme events which can cause large losses. The Pareto distribution is often used in actuarial sciences for modeling large losses. This thesis extends the study of Cai and Wei (2011) by considering a two-line business model with positive dependence through stochastic ordering (PDS) risks, where the risks are bivariate Pareto distributed. Cai and Wei (2011) showed that in individual reinsurance treaties the excess-of-loss treaty is the optimal reinsurance form for an insurer with PDS risks. We derive explicit expressions for the optimal retention levels in the excess-of-loss treaty by considering several risk functions including the criteria of minimizing the variance, minimizing moments of higher order and minimizing moments of fractional order of the total retained loss of the insurer. This will be followed by a comparison of retentions for different choices of the parameters of the bivariate Pareto distribution.