@article {BernardGhossoub2010, title = {Static Portfolio Choice under Cumulative Prospect Theory}, journal = {Mathematics and Financial Economics}, volume = {2}, number = {4}, year = {2010}, pages = {277-306}, abstract = {

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{\textquoteright}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.

}, url = {https://link.springer.com/article/10.1007\%2Fs11579-009-0021-2}, author = {C Bernard and M Ghossoub} }