Pricing Catastrophe Excess of Loss Reinsurance Using Power Curves and the Generalized Logarithmic Mean

This paper advocates use of the generalized logarithmic mean as the midpoint of property catastrophe reinsurance layers when fitting rates on line with power curves. It demonstrates that the method is easy to implement and overcomes issues encountered when working with usual candidates for the midpoint, such as the arithmetic, geometric, or logarithmic mean. The paper shows how to deal with paid reinstatements in a simplified framework and also introduces a new midpoint that is consistent with a negative exponential fit of the rates on line.