A Stochastic Programming Framework for Multi-period Portfolio Optimization

Abstract

This paper presents a scenario-based multistage stochastic programming model to deal with multi-period portfolio optimization problem with cardinality constraints and proportional transaction costs. The presented model aims to minimize investor's expected regret, while setting a minimum level of expected return. To generate the scenario tree of stochastic parameters, a random walk model based on Johnson transformation and a sampling procedure is used. To implement the scenario tree generation method, historical returns of 28 domestic indices are used. Then, the scenario tree of stochastic parameters are used to solve the proposed multistage stochastic programming model. In addition, the impact of transaction costs, minimum expected returns and predetermined target wealth are investigated. Numerical results show that transaction costs, minimum expected returns and target wealth have a direct impact on expected regret. Finally, back testing simulation is used to assess and analyze the impact of the proposed approach in a dynamic, multi-period setting.

Keywords

• scenario-based multistage stochastic programming
• multi-period portfolio optimization
• scenario tree
• random walk model
• johnson transformation