Research On Pension Investment Under Stochastic Interest Rate And Stochastic Volatility Model

The investment is risky, with the development of economy, we need to avoid risks and improve yield through the portfolio, and to find the optimal investment strategy in the portfolio. In a real stock market, there are many uncertain factors, such as the financial crisis, natural disaster, can produce a great impact on the stock returns; Otherwise, the securities investment also has certain risk and the investment risk can be divided into two categories, namely the economic risk and psychological risks. The main risk of bond investment is the economic risk, which considers from the securities issuers to liquidate risk, the risk of default, and the interest rate risk and inflation risk of the stock market, etc. So on the condition that the yield and the variance of the risky assets are random, it is necessary to study the optimal investment strategy. According to the current situation of financial markets, investors can put money to invest in zero-coupon bonds, risk-free assets and stock.In this study, there are two main study results. At first, we study the dy-namics optimal portfolios with CIR interest rate under a Heston model, which aims at maximizing the expected utility of the terminal. By applying dynamic programming principle, the explicit solutions of optimal portfolio strategy for con-stant relative risk aversion(CRRA) utility are achieved successfully. Finally, some numerical examples is presented to characterize the dynamic behavior of optimal portfolio strategy. Next, we study the optimal portfolios for DC pension plans under the stochastic interest rate and stochastic volatility model maximizing a HARA utility. By applying the Legendre transform, we obtain the optimal in-vestment strategy of the expected wealth maximum utility, and get some special examples.