Reciprocal reinsurance treaties seen as a two-person co-operative game

Abstract

Abstract 1.1. In 1930 Professor Cramer wrote: "The object of the theory of risk is to give a mathematical analysis of the random fluctuations in an insurance business, and to discuss the various means of protection against their inconvenient effects" ([6], page 7). This definition has obviously been adequate, since Cramer still subscribes to it when 25 years later he makes a comprehensive survey of the subject [7]. However, the mild complaint Cramer made in 1930 that "practical insurance business has hitherto made little or no application of the results offered by the mathematical theory of risk" still has some validity. The very impressive results achieved by the mathematical theory of risk during the last thirty years have certainly found practical applications, but not so many as one would expect, considering that the theory proposes to analyse the very foundations of the insurance business.