A generalized multi-period mean–variance portfolio optimization with Markov switching parameters

• Published in: Automatica (Oxford) Vol. 44; no. 10; pp. 2487 - 2497
• Main Authors: Costa, Oswaldo L.V., Araujo, Michael V.
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01.10.2008; Elsevier
• Subjects: Applied sciences; Decision theory. Utility theory; Exact sciences and technology; Firm modelling; Generalized mean–variance; Markov chain; Multi-period; Operational research and scientific management; Operational research. Management science; Optimal control; Portfolio optimization; Portfolio theory; Stochastic systems; Markov chain; Portfolio optimization; Stochastic systems; Multi-period; Generalized mean–variance; Optimal control; Markov process; Necessary and sufficient condition; Optimal policy; Transaction processing; Difference equation; Modeling; Switching; Selection problem; Uncertain system; Portfolio selection; Automatic control; Recursive method; Set theory; Riccati equation; Risk management; Generalized mean-variance; Portfolio management; Bankruptcy
• ISSN: 0005-1098; 1873-2836
• DOI: 10.1016/j.automatica.2008.02.014

In this paper, we deal with a generalized multi-period mean–variance portfolio selection problem with market parameters subject to Markov random regime switchings. Problems of this kind have been recently considered in the literature for control over bankruptcy, for cases in which there are no jumps in market parameters (see [Zhu, S. S., Li, D., & Wang, S. Y. (2004). Risk control over bankruptcy in dynamic portfolio selection: A generalized mean variance formulation. IEEE Transactions on Automatic Control, 49, 447–457]). We present necessary and sufficient conditions for obtaining an optimal control policy for this Markovian generalized multi-period mean–variance problem, based on a set of interconnected Riccati difference equations, and on a set of other recursive equations. Some closed formulas are also derived for two special cases, extending some previous results in the literature. We apply the results to a numerical example with real data for risk control over bankruptcy in a dynamic portfolio selection problem with Markov jumps selection problem.