Mean-variance model for portfolio optimization problem in the simultaneous presence of random and uncertain returns.

•We first propose a hybrid portfolio optimization problem with mixture of random returns and uncertain returns.•We give the analytical forms of variance of the portfolio return based on uncertain random variable.•We present mean-variance models for hybrid portfolio optimization and translate them into convex quadratic programming.•We consider the solution procedures and give the analytical solutions in the case with no more than two new securities.