A "square-root rule" for reinsurance

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).

A simulation of the insurance industry: the problem of risk model homogeneity

“…While this can offer some basic guidance on modeling specific elements of insurance markets, their value for system-level analyses and for predictions is limited due to strong assumptions. An example is the hypothesis of the "square-root rule of reinsurance" (Powers and Shubik 2006), that derives the optimal relation of the number of reinsurers to that of insurers as following a square-root function of the size of the system. While the empirical relationship is indeed sub-linear, studies (Venezian et al 2005;Du et al 2015) cannot confirm the exact square-root nature.…”

Competition among non-life insurers under solvency constraints: A game-theoretic approach

“…They also study scale effects of the number of insurers on the premium equilibrium. Powers & Shubik (2006) include reinsurers as additional players and study the optimal number of reinsurers in an insurance market. The present paper aims to model competition in non-life insurance markets with noncooperative game theory in order to extend the insurer-vs-market reasoning of Taylor (1986Taylor ( , 1987.…”

Human mortality: written in the stars?

“…The lesson in all this, of course, is that one does not have to be dealing with matters as funereal as death, or as ethereal as the solar system, to “discover” formal mathematical relationships where none in fact exist. Such excessively hopeful applications of analytic formulas abound in the study of insurance and other financial markets; and somewhat regretfully, I must confess to being as optimistic as anyone else (see Powers and Shubik, 2006).…”