摘要
Based on the Lie symmetry method,we derive the explicit optimal invest strategy for an investor who seeks to maximize the expected exponential(CARA)utility of the terminal wealth in a defined-contribution pension plan under a constant elasticity of variance model.We examine the point symmetries of the Hamilton-Jacobi-Bellman(HJB)equation associated with the portfolio optimization problem.The symmetries compatible with the terminal condition enable us to transform the(2+1)-dimensional HJB equation into a(1+1)-dimensional nonlinear equation which is linearized by its infinite-parameter Lie group of point transformations.Finally,the ansatz technique based on variables separation is applied to solve the linear equation and the optimal strategy is obtained.The algorithmic procedure of the Lie symmetry analysis method adopted here is quite general compared with conjectures used in the literature.
基金
supported in part by the 13th Five-Year National Key Research and Development Program of China(Grant No.2016YFCO401407)
the National Natural Science Foundation of China(Grant No.72071076)
the Beijing NaturalScience Foundation(Grant No.Z200001)
the Fundamental Research Funds of the Central Universities(Grant Nos.2019MS050,2020MS043).
