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On The Equivalence Of The Loss Ratio And Pure Premium Methods Of Determining Property And Casualty Rating Relativities, Robert L. Brown

Journal of Actuarial Practice (1993-2006)

There are two distinct stages in the property and casualty ratemaking process. First, there is the portfolio average rate change. Second, there is the adjustment of classification relativities. It is well known that the loss ratio and pure premium (also called the loss cost) methods are algebraically equivalent in the stage called the portfolio average rate change. This paper reviews the proof of this equivalence. Further, it is proved algebraically that the loss ratio and pure premium methods are also equivalent in calculating classification relativities (or differentials) if certain data requirements can be met. A short numerical example of this …