Risk measures beyond the variance have shown theoretical advantages when addressing some classical problems of Financial Economics, at least if asymmetries and/or heavy tails are involved. Nevertheless, in portfolio selection they have provoked several caveats such as the existence of good deals...

This paper deals with the optimal reinsurance problem if both insurer and reinsurer are facing risk and uncertainty, though the classical uncertainty free case is also included. The insurer and reinsurer degrees of uncertainty do not have to be identical. The decision variable is not the...

This paper deals with the optimal reinsurance problem and involves the goals of both insurer and reinsurer. An important novelty may be the incorporation of the background risk that the reinsurer uses in order to diversify (or hedge) the risk ceded by the insurer. Accordingly, general methods to...

Downside and deviation risk measures are becoming more and more important in many disciplines with clear interfaces with Applied Mathematics and Operations Research. Their dual representations have played critical roles in most of their applications (risk management, portfolio selection, pricing...