借贷利率限制下的效用投资组合

摘要

应用动态规划得到不同借贷利率情形下动态资产分配问题的HJB方程,并对指数效用、幂效用以及对数效用函数下的最优投资策略进行研究.通过求解相应的HJB方程和定义借入曲线得出最优投资组合的解析表达式,并对不同效用函数下投资者的借贷情况进行了说明.最后,给出算例对所得结论进行分析.%This paper focuses on a continuous-time dynamic portfolio selection problem with different interest rates for borrowing and lending. The Hamilton-Jacobi-Bellman (HJB) equations for utility maximizing criteria are derived by applying dynamic programming. Exponential utility and power utility and logarithm utility are assumed for our analysis. The closed-form solutions to the optimal portfolios are derived by solving HJB equations and introducing the borrowing curve. Finally, the situations of borrowing and lending for the investors are analyzed under three different utility functions and a numerical example is given to illustrate the results obtained.