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

By Jean-Francois Walhin

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Abstract

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

Citation

Walhin, Jean-Francois, "Pricing Catastrophe Excess of Loss Reinsurance Using Power Curves and the Generalized Logarithmic Mean," Variance 12:1, 2018, pp. 100-112.

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Mission Statement

Variance (ISSN 1940-6452) is a peer-reviewed journal published by the Casualty Actuarial Society to disseminate work of interest to casualty actuaries worldwide. The focus of Variance is original practical and theoretical research in casualty actuarial science. Significant survey or similar articles are also considered for publication. Membership in the Casualty Actuarial Society is not a prerequisite for submitting papers to the journal and submissions by non-CAS members is encouraged.