Abstract
In previous work, the 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 article, 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).
Highlights
In the past two decades, the global reinsurance market has experienced a period of rapid change
We show analytically that, fórlarge numbers ofprimary·insurers, this mathematical expression provides a."square-root rule"; i.e.,·theoptimal number ofreinsurers in a market is given asymptQticallyby the square root ofthe total number ofprimary insurCrs
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
Summary
In the past two decades, the global reinsurance market has experienced a period of rapid change. We first review the formal model of a primary insurance market presented in Powers, Shubik, and Yao (1998) and Powers and Shubik (1998). This model employs a Cournot price-formation mechanism with arbitrary numbers of buyers and sellers, 50 that marginal changes in insurer solvency and competitive forces can be studied directly as the numbers of players change. The random variable Oi equals 1 if customer i suffers a property 1055 during [O, t]. To recognize the possibility of insurer insolvency during [O, t), let t] be a Bernoulli random variable that equals 1 if in-. If there is an insolvency, it is assumed that government guaranty funds will pay a fixed proportion g E [O, 1) of ali insurance claims made against the insolvent insurer
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