The Optimal Investment Strategy For Defined-contribution Pension Plans

Optimal investment problem is the basis of financial economics asset pricing and risk management, and using stochastic mathematical methods to study and solve the optimal investment problem has become a hot study in mathematical finance. But the study on the optimal investment strategy for occupational pension is being in the initial stage at home and abroad The dissertation explored the optimal investment strategy for occupational pension founds based on former study.First the dissertation gives some preliminaries, and we explain the situation of study in our subject and simply introduce the basic concepts and theorems of the stochastic optimal control and the optimal investment problem. Then in a two-independent-asset world, we study the portfolio problem of manager who wants to maximize the expected utility of the terminal wealth in a complete financial market under the interest rate is a constant. Using the method of stochastic optimal control, we derive a non-linear second-order partial differential equation for the value function. As it is difficult to find a closed form solution, we transform the primary problem into a dual one by applying a Legendre transform and dual theory, and try to find an explicit solution for the optimal investment strategy under the logarithm utility function. Considering five kinds of assumptions on changes of Volatility and returns,a numerical Monte Carlo simulation is carried out to characterize the dynamic behavior of the optimal strategy. Furthermore, aiming at initial value of wealth and Contribution rate of pre-retirement annuity for the employee, sensitivity analysis is carried out . Finally, the conclusions came out and the future work was schemed out.