Multi-period uncertain portfolio optimization model with minimum transaction lots and dynamic risk preference

Abstract

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.