| Researches on the optimal portfolio of DC pension plan can effectively improve the investment return of the pension fund in the capital market,which will make a pension participants’ living standards not be seriously affected after retirement.This thesis mainly starts from the risk preference of pension managers and the background risks of financial markets,by using the stochastic optimal control method to discusses the investment decision issues of DC pension plan while the pension manager is ambiguity aversion,has limited attention problem,has the motion to break the pre-commitment,the pension managers and participants have misaligned goals.Firstly,this thesis considers the optimal portfolio of a DC pension manager who can invest in foreign assets.In the domestic market,the pension manager needs to consider the interest rate risk,inflation risk,and investment risk in the stock market.In foreign markets,the pension manager also needs to consider foreign interest rate risk and stock market risk.In addition,in order to hedge exchange rate risk,the pension manager needs to consider investing in exchange rate futures.We further assuming that the pension manager is ambiguity aversion,and the distribution of foreign assets is ambiguous.Using the entropy penalty method based on the robust control theory we obtain the optimal strategy.Secondly,this thesis considers the optimal portfolio problem of a pension manager with “limited attention”.Different from the traditional theory in which investors can acquire all information without paying any cost,this thesis considers that pension managers will incur costs while acquiring and processing information,which in turn limits the ability of pension managers to acquire and process information.Using Shannon’s information entropy theory to describe the process of interest rate and stock price in steady state,further,under the theory of Kalman filter and robust optimization theory,the optimal investment strategy of a pension manager is discussed.We found that when there is a“limited attention” situation,pension managers generally underestimate the volatility of asset prices and thus increase their exposure to risky assets.Thirdly,this thesis considers the optimal portfolio problem under mean variance criterion,with a manager who has the motivation to deviate from the initial commitment.Since the optimal investment decision under the classic time consistent framework contradict with the “conventional investment wisdom” in the financial market,this thesis considers maximizing the log return at the terminal time,and assumes that the contribution process of the pension participants is stochastic.Compared with the existing literature,the investment strategy obtained in this thesis satisfies the so-called “conventional investment wisdom” and is more in line with the real financial market.Finally,this thesis considers the situation where the goals of a pension manager and the participants are inconsistent under incentive schemes.By taking the strategy of the pension manager before and after the implementation of the incentive schemes as a benchmark,the corresponding Pareto optimal situation is considered.Under the consideration of Pareto optimal,pension manager have the characteristics of risk aversion for wealth above the reference level and risk preferences below the reference level,moreover,pension managers also exhibit risk aversion when facing extreme losses(that is,when the wealth level is approaching bankruptcy),this situation is more in line with the utility of pension manager in the general market. |
