An accurate variable description of security returns is necessary to establish a valid portfolio optimization model. It is usually assumed to be a random variable when the historical data of security returns are sufficient. However, when historical data are too limited to estimate its probability distribution, uncertain variables are employed to characterize security returns to be effective. This paper focuses on a multi-period portfolio optimization problem in uncertain environment with the consideration of minimum transaction lots. Different from the previous multi-period work assuming the total available wealth in the end of the investment horizon is consistently in an exponential format, our study provides a simplified additive format of the total wealth, which may make the process of experimental calculation concise, since it is a linear function of decision variables. Besides, we consider the investor’s dynamic risk preference along the whole investment horizon. With these realistic constraints derived from the complex financial markets, we build a multi-period mean-VaR (value-at-risk) model with the objective of maximizing the terminal wealth under the risk control over the whole investment. Genetic algorithm is used to solve the proposed model, and two numerical examples are given to illustrate the effectiveness of the proposed approach.

证券收益的准确变量描述对于建立有效的投资组合优化模型是必要的。当证券收益的历史数据充足时，通常假设它是一个随机变量。然而，当历史数据太有限而无法估计其概率分布时，使用不确定变量来表征证券收益是有效的。本文着眼于考虑最小交易手数的不确定环境下的多周期投资组合优化问题。与之前的多期工作假设投资期限结束时的总可用财富始终呈指数格式不同，我们的研究提供了一种简化的总财富加法格式，这可能会使实验计算过程更加简洁，因为它是决策变量的线性函数。此外，我们考虑了投资者在整个投资期限内的动态风险偏好。基于复杂金融市场衍生的这些现实约束，我们构建了多周期均值-VaR（value-at-risk）模型，目标是在整个投资的风险控制下最大化终端财富。采用遗传算法对所提出的模型进行求解，并给出两个数值算例来说明所提出方法的有效性。我们建立了一个多周期均值-VaR（value-at-risk）模型，目标是在整个投资的风险控制下最大化终端财富。采用遗传算法对所提出的模型进行求解，并给出两个数值算例来说明所提出方法的有效性。我们建立了一个多周期均值-VaR（value-at-risk）模型，目标是在整个投资的风险控制下最大化终端财富。采用遗传算法对所提出的模型进行求解，并给出两个数值算例来说明所提出方法的有效性。