Adding independent risks in an insurance portfolio:which shape for the insurers' preferences?

Many papers in the litterature have adopted the expected utility paradigm to analyze insurancedecisions. Insurance companies manage policies by growing, by adding independent risks.Even if adding risks generally ultimately decreases the probability of insolvency, the impacton the insurer's expected utility is less clear. Indeed, it is not true that the risk aversion towardthe additional loss generated by a new policy included in an insurance portfolio is adecreasing function of the number of contracts already underwritten (i.e. the "fallacy of largenumbers"). In this paper, it is shown that most commonly used utility functions do notnecessarily positively value the aggregation of independent risks so that they are not éligiblefor insurers. This casts some doubt about the conclusions drawn in the papers postulating suchcompletely monotonic utilities for guiding insurers' choices. Finally, it is shown that thesufficient conditions for adding risks that can be found in the litterature need to be refined byrestricting the domain of définition of the insurer's utility function....