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This paper is devoted to invest an optimal investment strategy for adefined-contribution (DC) pension plan under the Ornstein-Uhlenbeck (O-U)process and the loan. By considering risk-free asset, a risky asset driven byO-U process and a loan in the financial market, we firstly set up the dynamicequation and the asset market model which are instrumental in achieving theexpected utility of ultimate wealth at retirement. Secondly, the correspondingHamilton-Jacobi-Bellman(HJB) equation is derived by means of dynamicprogramming principle. The explicit expression for the optimal investmentstrategy is obtained by Legendre transform method. Finally, differentparameters are selected to simulate the explicit solution and the financialinterpretation of the optimal investment strategy is given.

The optimal investment strategy of a DC pension plan under deposit loan spread and the O-U process