A unifying approach to constrained and unconstrained optimal reinsurance
In this paper, we study two classes of optimal reinsurance models from
perspectives of both insurers and reinsurers by minimizing their convex
combination where the risk is measured by a distortion risk measure and the
premium is given by a distortion premium principle. Firstly, we show that how
optimal reinsurance models for the unconstrained optimization problem and
constrained optimization problems can be formulated in a unified way. Secondly,
we propose a geometric approach to solve optimal reinsurance problems directly.
This paper considers a class of increasing convex ceded loss functions and
derives the explicit solutions of the optimal reinsurance which can be in forms
of quota-share, stop-loss, change-loss, the combination of quota-share and
change-loss or the combination of change-loss and change-loss with different
retentions. Finally, we consider two specific cases: Value at Risk (VaR) and
Tail Value at Risk (TVaR).