A note on optimal insurance risk control with multiple reinsurers

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.