A Note on a "Square-Root Rule" for Reinsurance

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).