Multi-period investment decision problem based on time consistent generalized convex risk measure and extremum scenarios

Abstract

Purpose – To help investors find an investment policy with strong competitiveness, the purpose of this paper is to construct a multi-period investment decision model with practicality and superior performance. Design/methodology/approach – The paper uses a suitable multi-period risk measure to construct a multi-period portfolio selection model, where target returns at intermediate periods and market frictions are taken into account simultaneously. An efficient scenario tree generation approach is proposed in order to transform the complex multi-period portfolio selection problem into a tractable one. Findings – Numerical results show the new scenario tree generation algorithms are stable and can further reduce the tree size. With the scenario tree generated by the new scenario tree generation approach, the optimal investment strategy obtained under the multi-period investment decision model has more superior performance and robustness than the corresponding optimal investment strategy obtained under the single period investment model or the multi-period investment model only paying attention to the terminal cash flow. Research limitations/implications – The new risk measure and multi-period investment decision models can stimulate readers to find even better models and to efficiently solve realistic multi-period portfolio selection problems. Practical implications – The empirical results show the superior performance and robustness of optimal investment strategy obtained with the new models. What's more important, the empirical analyses tell readers how different market frictions affect the performance of optimal portfolios, which can guide them to efficiently solve real multi-period investment decision problems in practice. Originality/value – The paper first derives the concrete structure of the time consistent generalized convex multi-period risk measure, then constructs a multi-period portfolio selection model based on the new multi-period risk measure, and proposes a new extremum scenario tree generation algorithm. The authors construct a realistic multi-period investment decision model. Furthermore, using the proposed scenario tree generation algorithm, the authors transform the established stochastic investment decision model into a deterministic optimization problem, which can provide optimal investment decisions with robustness and superior performance.