Optimal Portfolios for DC Pension under the Quadratic Utility Function

The optimal investment strategies of defined-contribution pension under the quadratic utility function are studied in the paper. In our model, the plan member is allowed to invest in a risk-free asset and a risky asset, which is described by a constant elasticity of variance (CEV) model. By applying Legendre transform and dual theory, the non-linear second partial differential equation is transformed into a linear partial differential equation in order that the explicit solution for the quadratic utility function is found. The result shows that the optimal proportion invested in risky assets for the pension investor with the exponential utility function is divided into three parts: moving Merton factor, correction factor, contributions´ factor and the correction factor is a monotone decreasing function with respect to time t.