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...

This paper proposes a new method to introduce coherent risk measures for risks with infinite expectation, such as those characterized by some Pareto distributions. Extensions of the conditional value at risk, the weighted conditional value at risk and other examples are given. Actuarial...