In this paper, we propose new risk measures from a regulator's perspective on the regulatory capital requirements for insurers. The proposed risk measures possess many desired properties including monotonicity, translation-invariance, positive homogeneity, subadditivity, nonnegative loading, and...

Worst-case risk measures refer to the calculation of the largest value for risk measures when only partial information of the underlying distribution is available. For the popular risk measures such as Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR), it is now known that their...

The theory of convex risk functions has now been well established as the basis for identifying the families of risk functions that should be used in risk-averse optimization problems. Despite its theoretical appeal, the implementation of a convex risk function remains difficult, as there is...