Pricing Catastrophe Excess of Loss Reinsurance Using Power Curves and the Generalized Logarithmic Mean
By Jean-Francois Walhin
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.
Keywords Midpoint, arithmetic mean, geometric mean, logarithmic mean, generalized logarithmic mean, Pareto distribution, rate on line, reinstatement, survival function, property catastrophe excess of loss reinsurance, power curve, negative exponential curve