Portfolio Optimization Under the Uncertain Financial Model

The purpose of this paper is to employ the fractional uncertain differential equation to model stock price and design an strategy to reduce the investment risk based on the optimization model. First, the two-factor fractional Liu uncertain model with the renewal process is presented. Then two algorithms are proposed to identify and separate the jump data and by using the properties of the fractional Liu and the renewal processes, formulas are derived to calibrate the model's parameters based on the NASDAQ market data. After that, to reduce the unsystematic investment risk, a normalized version of the CCMV optimization model is introduced to the investment portfolio diversification. To improve the performance of the portfolio optimization model, the financial model is applied to predict the future of the stock prices and find their rate of returns and covariance matrix and apply them as the input of the model. Finally, the numerical results show the efficiency of the model and the presented investment strategy.