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

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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).

Suggested Citation

  • Michael R. Powers & Martin Shubik, 2005. "A Note on a "Square-Root Rule" for Reinsurance," Cowles Foundation Discussion Papers 1521, Cowles Foundation for Research in Economics, Yale University.
  • Handle: RePEc:cwl:cwldpp:1521
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    File URL: http://cowles.yale.edu/sites/default/files/files/pub/d15/d1521.pdf
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    Keywords

    Primary insurance; Reinsurance; Market size; Square-root rule;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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