A Constant Elasticity of Variance (CEV) Model and Legendre Transform-Dual Solution for Defined Benefit Pension Funds Management
养老基金管理的常方差弹性模型及Legendre 变换2对偶解法

This paper presents a constant elasticity of variance model for defined pension funds management,obtains the non-linear Hamilton-Jacobi-Bellman partial differential equation,and reduces to a linear partial differential equation and the dual problems with the Legendre transform.We give the analytic solutions of the primal optimal problem by studying the dual problem.So we can find an optimal asset allocation-between a risky asset and a riskless asset-and the least contribution policy.