A note on optimal insurance risk control with multiple reinsurers

Abstract

This note revisits the problem discussed in Meng et al. (2016) where an optimal insurance risk control problem was considered in a diffusion approximation model with multiple reinsurers adopting variance premium principles. It was shown in Meng et al. (2016) that under a certain technical condition, a combined proportional reinsurance treaty is an optimal form in a class of plausible reinsurance treaties. From both theoretical and practical perspectives, an interesting question may be whether the combined proportional reinsurance treaty is still an optimal form in a quite considerably larger class of plausible reinsurance treaties. This note addresses this question and shows that a combined proportional reinsurance treaty is still an optimal form.