PROCEEDINGS May 15, 16, 17, 18, 2005 - Casualty Actuarial Society

RISKINESS LEVERAGE MODELSRODNEY KREPSAbstractA general formulation of risk load for total cash flowsis presented. It allows completely additive co-measures 1at any level of detail for any dependency structurebetween random variables constituting the total. It isfounded on the intuition that some total outcomes aremore risky per dollar than others, and the measure ofthat is a “riskiness leverage ratio.” This riskiness leveragefunction is an essentially arbitrary choice, enablingan infinite variety of management attitudes toward riskto be expressed.The complete additivity makes these models useful.What makes them interesting is that attention can beturned toward asking “What is a plausible risk measurefor the whole, while being prepared to use the indicatedallocation technique for the pieces?” The usual measuresare special cases of this form, as shown in someexamples.While the author does not particularly advocate allocatingcapital to do pricing, this class of models doesallow pricing at the individual policy clause level, if sodesired.Further, the desirability of reinsurance or otherhedges can be quantitatively evaluated from the cedant’spoint of view by comparing the increase in the mean costof underwriting with the decrease in capital cost fromreduction of capital required.1 Gary Venter coined this term, in parallel with variance and covariance.31