Portfolio selection based on uncertain fractional differential equation

Portfolio selection problems are considered in the paper. The securities in the proposed problems are suggested to follow uncertain fractional differential equations which have memory characteristics. By introducing the left semi-deviation of the wealth, two problems are proposed. One is to maximize the expected value and minimize the left semi-variance of the wealth. The other is to maximize the expected value of the wealth with a chance constraint that the left semi-deviation of the wealth is not less than a given number at a confidence level. The problems are equivalent to determinant ones which will be solved by genetic algorithm. Examples are provided to show the effectiveness of the proposed methods.