Portfolio selection with quadratic utility function under fuzzy enviornment

Uncertainty is present in real financial markets due to unknown events, such as return streams, prices of securities, maintenance costs etc. Usually, uncertainty includes two aspects: randomness and fuzziness. Famous Markowitz's portfolio selection model deals with uncertainty using probability approach. But it is not enough to describe the real financial markets. This paper considers the return rate as a fuzzy number and assume all investors are risk averse, who make investment decisions according to maximize utility score. The score is given by the Von-Neumann-Morgenstern utility function, which is a quadratic function. We will propose an n-asset portfolio selection model based on possibilistic mean and possibilistic variance and discuss its optimal solution.