Riskiness Leverage Models

A general formulation of risk load for total cash flows is presented. It allows completely additive co-measures at any level of detail for any dependency structure between random variables constituting the total. It is founded on the intuition that some total outcomes are more risky per dollar than others, and the measure of that is a “riskiness leverage ratio.” This riskiness leverage function is an essentially arbitrary choice, enabling an infinite variety of management attitudes toward risk to be expressed. The complete additivity makes these models useful. What makes them interesting is that attention can be turned toward asking “What is a plausible risk measure for the whole, while being prepared to use the indicated allocation technique for the pieces?” The usual measures are special cases of this form, as shown in some examples. While the author does not particularly advocate allocating capital to do pricing, this class of models does allow pricing at the individual policy clause level, if so desired. Further, the desirability of reinsurance or other hedges can be quantitatively evaluated from the cedant’s point of view by comparing the increase in the mean cost of underwriting with the decrease in capital cost from reduction of capital required.