Pricing to Optimize an Insurer's Risk-Return Relation

It is appealing to estimate loss discount rates and risk loads for categories of an insurer’s premium by using the categories’ contributions to surplus variation. However, as will be explained, there has been a theoretical obstacle to this approach. This paper presents a method that overcomes the obstacle. It produces a surprisingly simple result. The risk load (in dollars) of a category is proportional to the covariance of the yearly return on surplus with the category’s yearly profit. The paper analyzes the use of the above result to optimize an insurer’s risk-return relation. Some examples of computation of 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. Keyword: Profit, Risk