| In the portfolio theory, the optimal portfolio problem has always been a hot topic for scholars. At first, the portfolio theory was developed under the framework of linear expectations, but the investment portfolio under the linear expectation framework also had some limitations due to uncertainties in the real financial environment and investor preferences.Therefore, we need to further study the portfolio problem in the framework of non-linear expectation. Meanwhile, the diversification of financial products also requires us to take the securities into consideration of the portfolio problem. This paper mainly studies two problems: one in the framework of linear expectation, the dynamic investment portfolio of stocks and bonds based on stochastic interest rate and time-varying volatility is simply studied. The other is based on the stochastic interest rate and time-varying volatility stock, bonds and derivative securities.This paper is divided into five parts. Chapter 1 elaborates the research background, the domestic and foreign research present situation,the research content and the frame. Chapter2 prepares the dynamic programming method, utility function and three utility models, Ito integral and stochastic differential equations, g-expectation. Chapter 3 in the framework of linear expectation, the Hull-White stochastic interest rate and time-varying volatility are introduced in the third chapter.Finally, we give the expression of the optimal investment strategy under the power utility function. Chapter 4 in the framework of g-expectation,considering the Hull-Hhite stochastic interest rate and time-varying volatility, the investment object takes into account the derivative securities in addition to the stocks and bonds. Finally, we give the expression of the optimal investment strategy under the power function and exponential utility function. Chapter 5 summarizes and prospects the full text, and explains the shortcomings of this paper and the future research directions. |
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