Pricing to Optimize an Insurer's Risk-Return Relation

The idea of estimating loss discount rates and risk loads for categories of an, insurer’s premium by using the categories’ contributions to surplus variation is an appealing one. However, there has been a theoretical obstacle to this approach, as will be explained in this paper. A method which overcomes the obstacle will be presented. It produces a surprisingly simple result. The risk load (in dollars) of a category is proportional to the covariance of the category’s profit with surplus. The use of the above result to optimize an insurer’s risk-return relation is analyzed in the paper. Some examples of applications .of the result to compute risk loads and risk-based discount rates for losses are presented. The relationship between the method of this paper, the Capital Asset Pricing Model, and several other models is discussed.