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

Michel M. Denuit, Louis Eeckhoudt and Mario Menegatti
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Michel M. Denuit: UNIVERSITE CATHOLIQUE DE LOUVAIN, Institut de Sciences Actuarielles & Institut de Statistique

No 2009008, LIDAM Discussion Papers CORE from Université catholique de Louvain, Center for Operations Research and Econometrics (CORE)

Abstract: Many papers in the litterature have adopted the expected utility paradigm to analyze insurance decisions. Insurance companies manage policies by growing, by adding independent risks. Even if adding risks generally ultimately decreases the probability of insolvency, the impact on the insurer's expected utility is less clear. Indeed, it is not true that the risk aversion toward the additional loss generated by a new policy included in an insurance portfolio is a decreasing function of the number of contracts already underwritten (i.e. the "fallacy of large numbers"). In this paper, it is shown that most commonly used utility functions do not necessarily positively value the aggregation of independent risks so that they are not éligible for insurers. This casts some doubt about the conclusions drawn in the papers postulating such completely monotonic utilities for guiding insurers' choices. Finally, it is shown that the sufficient conditions for adding risks that can be found in the litterature need to be refined by restricting the domain of definition of the insurer's utility function.

Keywords: expected utility; compensating premium; prudence; temperance (search for similar items in EconPapers)
Date: 2009-02-01
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Working Paper: Adding independent risks in an insurance portfolio: wich shape for the insurer's preferences? (2010)
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