不完全市场下基于对数效用的动态投资组合

应用鞅方法研究不完全市场下的动态投资组合优化问题。首先,通过降低布朗运动的维数将不完全金融市场转化为完全金融市场,并在转化后的完全金融市场里应用鞅方法研究对数效用函数下的动态投资组合问题,得到了最优投资策略的显示表达式。然后,根据转化后的完全金融市场与原不完全金融市场之间的参数关系,得到原不完全金融市场下的最优投资策略。算例分析比较了不完全金融市场与转化后的完全金融市场下最优投资策略的变化趋势,并与幂效用、指数效用下最优投资策略的变化趋势做了比较。

Dynamic Portfolio Selection for Logarithm Utility Maximization in an Incomplete Market

This paper applies martingale approach to study a dynamic portfolio selection problem in an incomplete market.By reducing the dimension of Brownian motion,we transform an incomplete market into a complete one and use martingale approach to investigate the optimal investment strategy for logarithm utility maximization in the completed market,In addition,we obtain the explicit expression of the optimal investment strategy.We derive the optimal investment strategy in the original incomplete market by applying the parameters relationships between in the original incomplete market and in the completed one.Numerical examples are given to compare the optimal portfolios for logarithm utility with those for power utility and exponential utility both in a complete market and in an incomplete one.