Distorted expectations can be expressed as weighted averages of quantiles. In this note, we show that this statement is true, but that one has to be careful with the correct formulation of it. Furthermore, the proofs of the additivity property for distorted expectations of a comonotonic sum that...

The computation of various risk metrics is essential to the quantitative risk management of variable annuity guaranteed benefits. The current market practice of Monte Carlo simulation often requires intensive computations, which can be very costly for insurance companies to implement and take so...