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.