| Abstract: |
In previous work, the current authors derived a mathematical expression for
the optimal (or "saturation") number of reinsurers for a given number of
primary insurers (see Powers and Shubik, 2001). In the current paper, we show
analytically that, for large numbers of primary insurers, this mathematical
expression provides a "square-root rule"; i.e., the optimal number of
reinsurers in a market is given asymptotically by the square root of the total
number of primary insurers. We note further that an analogous “fourth-root
rule” applies to markets for retrocession (the reinsurance of reinsurance). |