Comparing Risk Adjusted Premiums from the Reinsurance Point of View

Abstract

In this paper we compare, from the point of view of reinsurance, the several risk adjusted premium calculation principles considered in Wang (1996b). We conclude that, with the exception of the proportional hazard (PH) premium calculation principle, all the others behave in a way similar to the expected value principle. We prove that the stop loss reinsurance premium when calculated using the PH premium principle gives a higher premium than any of the other transforms, provided that the priority is big enough. We observe a similar behaviour with respect to excess of loss reinsurance in all the examples given.We also study the behaviour of the adjustment coefficient, both from the insurer's and the reinsurer's point of view as functions of the priority, when the PH principle is used as opposed to the expected value principle.