Theory and Decision

, Volume 80, Issue 2, pp 227–243 | Cite as

Risk aversion, prudence, and asset allocation: a review and some new developments

  • Michel M. Denuit
  • Louis Eeckhoudt


In this paper, we consider the composition of an optimal portfolio made of two dependent risky assets. The investor is first assumed to be a risk-averse expected utility maximizer, and we recover the existing conditions under which all these investors hold at least some percentage of their portfolio in one of the assets. Then, we assume that the decision maker is not only risk-averse, but also prudent and we obtain new minimum demand conditions as well as intuitively appealing interpretations for them. Finally, we consider the general case of investor’s preferences exhibiting risk apportionment of any order and we derive the corresponding minimum demand conditions. As a byproduct, we obtain conditions such that an investor holds either a positive quantity of one of the assets (positive demand condition) or a proportion greater than 50 % (i.e., the “50 % rule”).


Optimal portfolio Diversification Risk aversion  Downside risk Prudence Risk apportionment 



The financial support of PARC “Stochastic Modelling of Dependence” 2012–2017 awarded by the Communauté française de Belgique is gratefully acknowledged by Michel Denuit.


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Institut de Statistique, Biostatistique et Sciences Actuarielles (ISBA)Université Catholique de LouvainLouvain-la-NeuveBelgium
  2. 2.IESEG School of Management LEMLilleFrance
  3. 3.CORE Université Catholique de LouvainLouvain-la-NeuveBelgium

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