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本文研究了在交易成本约束下的基金财富动态最优增长.我们建立了基于Kelly理论的投资组合模型,它能确保采用该模型的基金的财富长期沿最优路径增长.随着投资组合中资产数量增加,目标函数变得非常复杂,如果按照Kelly原始的表达方式,模型无法求解.本文利用大数定律与对数效用函数可加性推导了连续时间情形下投资组合中资产的最优资金配置比例,并分析了模型的性质和效用函数.基于期货市场高频数据的实证结果显示该模型具有较高实用价值.
This paper studies the dynamic optimal growth of fund wealth under the transaction cost constraint.We establish a portfolio model based on Kelly theory to ensure that the wealth of the fund using the model grows along the optimal path.With the investment in the assets The number of objective function becomes very complicated, and the model can not be solved according to the original expression of Kelly.In this paper, by using the Law of Large Numbers and the logarithmic utility function, the optimal capital allocation of assets under continuous time can be deduced Ratio, and analyzes the nature of the model and the utility function.Experimental results based on high-frequency data in the futures market show that the model has high practical value.