Static portfolio choice under cumulative prospect theory

Carole Bernard, Mario Ghossoub

Research output: Contribution to journalArticle

70 Citations (Scopus)


We derive the optimal portfolio choice for an investor who behaves according to Cumulative Prospect Theory (CPT). The study is done in a one-period economy with one risk-free asset and one risky asset, and the reference point corresponds to the terminal wealth arising when the entire initial wealth is invested into the risk-free asset. When it exists, the optimal holding is a function of a generalized Omega measure of the distribution of the excess return on the risky asset over the risk-free rate. It conceptually resembles Merton's optimal holding for a CRRA expected-utility maximizer. We derive some properties of the optimal holding and illustrate our results using a simple example where the excess return has a skew-normal distribution. In particular, we show how a CPT investor is highly sensitive to the skewness of the excess return on the risky asset. In the model we adopt, with a piecewise-power value function with different shape parameters, loss aversion might be violated for reasons that are now well-understood in the literature. Nevertheless, we argue that this violation is acceptable.

Original languageEnglish
Pages (from-to)277-306
Number of pages30
JournalMathematics and Financial Economics
Issue number4
Publication statusPublished - 1 Mar 2010


  • Cumulative Prospect Theory
  • Omega measure
  • Portfolio choice

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