N Risk Assets To Determine The Contributory Pensions Optimal Investment Strategy

In practice of pension planning, much attention is paid to maintain and increase the value of pensions. One of the reasonable choices for the purpose is to invest pensions into risky market. However, risky investment can be dangerous. Therefore, one should choose a proper investment strategy to avoid the risks and to maximize the earnings. Since in a real market, there are usually multiple choices of risky asset, with different returns and volatilities which will result in different influences in making the investment strategy, and in addition, there are transaction costs in the transaction process as well, thus, to optimize the investment strategy for investing in multiple risky assets with transaction costs is of important significance both in theory and in practice.In this thesis, we study the optimization of investment strategies for Defined Contribution Pension. In chapter 3, the pension fund is supposed to invest in one risk-free asset and n species of risky assets, where the transaction costs are not taken into account. Mathematical models are established for the investment plans for the time before and after retirement, respectively. By using the dynamic programming method in stochastic optimal control theory, the corresponding optimal investment strategies in the sense of maximizing the exponential utility function and power utility function are obtained respectively. In chapter 4, the same problems are studied and similar conclusions are obtained when transaction costs are considered. We notice that, throughout chapter 3 and 4, the interest rate of the risk-free asset, the earnings and the variances of the risky assets there are all assumed to be constant.