Fractional programming model for portfolio with probability criterion

The problem of portfolio selection with probability criterion is investigated in this paper. The stochastic programming model for this problem is established. It is to maximize the probability that the return rate of the portfolio is no less than a given expect rate. The deterministic equivalent model of the stochastic programming is given under the condition that the return rate of the securities has normal distribution. Since the objective function in the deterministic equivalent fractional programming model is not a convex one, the traditional optimization techniques are no longer valid for solving this problem. In this paper, a method based on a genetic algorithm for solving the portfolio problem with probability criterion is proposed. Finally, an illustrative example is given and the effectiveness of the proposed solving method is shown.