Markowitz's Mean-Variance Portfolio Selection with Regime Switching: A Continuous-Time Model

A continuous-time version of the Markowitz mean-variance portfolio selection model is proposed and analyzed for a market consisting of one bank account and multiple stocks. The market parameters, including the bank interest rate and the appreciation and volatility rates of the stocks, depend on the...

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Bibliographic Details
Published in:SIAM journal on control and optimization 2003-01, Vol.42 (4), p.1466-1482
Main Authors: Zhou, Xun Yu, Yin, G.
Format: Article
Language:English
Subjects:
Brownian motion
Expected utility
Hedging
Interest rates
Lagrange multiplier
Markov analysis
Optimization
Stocks
Utility functions
Volatility
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Summary:A continuous-time version of the Markowitz mean-variance portfolio selection model is proposed and analyzed for a market consisting of one bank account and multiple stocks. The market parameters, including the bank interest rate and the appreciation and volatility rates of the stocks, depend on the market mode that switches among a finite number of states. The random regime switching is assumed to be independent of the underlying Brownian motion. This essentially renders the underlying market incomplete. A Markov chain modulated diffusion formulation is employed to model the problem. Using techniques of stochastic linear-quadratic control, mean-variance efficient portfolios and efficient frontiers are derived explicitly in closed forms, based on solutions of two systems of linear ordinary differential equations. Related issues such as a minimum-variance portfolio and a mutual fund theorem are also addressed. All the results are markedly different from those for the case when there is no regime switching. An interesting observation is, however, that if the interest rate is deterministic, then the results exhibit (rather unexpected) similarity to their no-regime-switching counterparts, even if the stock appreciation and volatility rates are Markov-modulated.
ISSN:0363-0129
1095-7138
DOI:10.1137/S0363012902405583