Optimal Investment Problem For A Pension Plan With Mispricing Under The Stochastic Volatility Model

Pension fund is one of the basic social security funds paid by the people nowadays.It is the main economic guarantee for the retired people.It is of great significance to the economic development and social stability of our country.With the rise of the economy and the development of our country,the proportion of the population in our country is unbalanced,and the aging problem is becoming more and more serious.At the same time,the economic market has a high inflation rate.Therefore,the traditional management mode of pension funds has greatly depreciated the value of pension funds.Investing pension funds in financial market can not only increase the value of pension funds to a certain extent,but also contribute to the balanced development of economy.Therefore,this paper considers the investment management of pension funds.We calculate the optimal investment strategy of pension funds in the market,and combines the experience analysis of the current situation of pension investment at home and abroad.At last,the paper obtains reasonable suggestions on the future development direction of pension funds management in China.Based on the current financial market,this paper takes economic and financial policies into account.Recently,China has introduced a stock purchase policy,which allows investors to buy and sell stocks in the mainland market and the Hong Kong market at the same time.With the implementation of the policy in the market,the financial market is constantly changing.The price of the same stock in the two financial markets is different,and the fluctuation is also different.We define the price difference of a stock in different markets as mispricing.Duo to the mispricing phenomenon exists in financial markets,we considerate the mispricing into the investment problem of pension funds to make the model more realistic.In this paper,we consider the optimal investment of a defined contribution pension fund with mispricing under stochastic volatility model,in which the stock' price process is assumed to conform to Heston stochastic volatility model.This makes the model more realistic and increases the di culty of calculation.It is assumed that pension funds can be invested in a market index,a risk-free asset and a risk asset with mispricing.In order to maximize the expected utility of the terminal wealth,we consider exponential utility function and power utility function respectively in Chapter 3 and Chapter 4.Firstly,by using the It(?) formula,the stochastic differential equation is written.Then,the corresponding Hamilton-Jacobi-Bellman(HJB)equation is established by applying the principle of dynamic programming.Chapter 3 and Chapter 4 obtain the optimal investment strategy for exponential utility function and power utility function respectively,and finally get the analytical solution of the optimal investment strategy.By simulating and analyzing the influence of model parameters and mispricing on the optimal investment strategy,the numerical optimization can guide investment management of pension funds in practice.