Equilibrium strategy for a multi-period weighted mean-variance portfolio selection in a Markov regime-switching market with uncertain time-horizon and a stochastic cash flow

Hao Ge, Xingyi Li, Xun Li, Zhongfei Li

Research output: Journal article publicationJournal articleAcademic researchpeer-review

Abstract

This article considers a multi-period weighted mean-variance portfolio selection problem with uncertain time-horizon and a stochastic cash flow in a Markov regime-switching market. The random returns of risky assets and amount of the cash flow all depend on the states of a stochastic market which are assumed to follow a discrete-time Markov chain. Based on the conditional distribution of uncertain time-horizon caused by exogenous factors, we construct a more general mean-variance investment model. Within a game theoretic framework, we derive the equilibrium strategy and equilibrium value function in closed-form by applying backward induction approach. In addition, we show the equilibrium efficient frontier and discuss some degenerate cases. Finally, some numerical examples and sensitivity analysis are presented to illustrate equilibrium efficient frontiers and the effects of uncertain time-horizon on the equilibrium strategy and equilibrium efficient frontier as well as regime-switching and stochastic cash flow on the equilibrium efficient frontier.

Original languageEnglish
Pages (from-to)1-36
Number of pages36
JournalCommunications in Statistics - Theory and Methods
DOIs
Publication statusE-pub ahead of print - 25 Aug 2021

Keywords

  • equilibrium efficient frontier
  • equilibrium strategy
  • Markov regime-switching
  • multi-period weighted mean-variance portfolio selection
  • stochastic cash flow
  • Uncertain time-horizon

ASJC Scopus subject areas

  • Statistics and Probability

Cite this