Diffusion Model DC-type Annuity Optimal Investment Research - Jump On

The problem of optimal investment strategies of Defined Contribution Enterprise Pension, especially in the accumulation phase before retirement, is one of the hot topics in the Finance and Insurance fields. The research aims at maximizing the expected utility of employee’s total wealth when retiring and then providing the optimal investment strategy.Existing researches on optimal investment strategy of Defined Contribution Enterprise Pension usually base on the assumption that the risky assets which include wages comply with the Geometric Brown motion. However, the price of risky assets tend to be volatile because the shocks of the significant information and policy in the financial markets. Besides, the wage level of the pension holders is in random fluctuations as well and even sometimes grows in "leaps and bounds".Taking all these into account, this thesis, which can be regarded as a natural extension of such studies will study the optimal investment strategy of Defined Contribution Enterprise Pension upon the assumption that the risky assets and the random wage subject to the jump-diffusion model.First of all, the thesis assumes that the price process of risky assets obey the jump-diffusion model, and then study the optimal investment strategy of Defined Contribution Enterprise Pension. Under specific utility function. Firstly obtains the HJB equation according to the principle of dynamic programming and then with the use of Legendre transform and dual theory we can acquire the explicit solutions to the problem.Moreover, the paper will have further research under the consideration of the stochastic wage with random jumps. With the help of the framework of the mean-variance model and the optimal control theory, we study the investment strategy of Defined Contribution Enterprise Pension, and finally provide the efficient frontier for the portfolio.