The constant elasticity of variance (CEV) model and the Legendre transform–dual solution for annuity contracts

The paper focuses on the constant elasticity of variance (CEV) model for studying a defined-contribution pension plan where benefits are paid by annuity. It also presents the process by which the Legendre transform and dual theory can be applied to find an optimal investment policy for a participant’s whole life in the pension plan. Finally, it reveals two explicit solutions for the logarithm utility function in two different periods (before and after retirement). Hence, the optimal investment strategies in the two periods are obtained.