一类投资组合模型的对称解

Symmetry-Based Solution of a Portfolio Selection Model

研究了风险资产服从几何布朗运动的最优投资组合问题。借助于动态规划原理和李代数理论,得到了相应的HJB方程及值函数基于李对称的解析表达式,并给出了最优投资策略,最后通过待定系数法验证了结果的正确性。

The paper addresses the optimal portfolio selection problem which risky assets follows geometric Brownian motion.With the help of the dynamic programming principle and Lie algebra theory,we get the corresponding HJB equation,obtain the analytical expressions of the value function based on Lie symmetry,and present the optimal investment strategy.In the end,the undetermined coefficient method shows the validity of the result.