Markowitz's Mean-Variance Portfolio Selection With Regime Switching: From Discrete-Time Models to Their Continuous-Time Limits

IEEE Transactions on Automatic Control

Volumn 49, Issue 3, 2004, Pages 349-360

  Yin, G ^a   Zhou, Xun Yu ^b  

^a WAYNE STATE UNIVERSITY   (United States)

^b CHINESE UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

Discrete time model; Linear quadratic problem; Markov chain; Markowitz's mean variance portfolio selection; Singular perturbation; Switching diffusion

Indexed keywords

DYNAMIC PROGRAMMING; FINANCE; MARKOV PROCESSES; MATHEMATICAL MODELS; PERTURBATION TECHNIQUES; PROBLEM SOLVING; RANDOM PROCESSES; RISK ASSESSMENT;

DISCRETE-TIME MODEL; LINEAR-QUADRATIC PROBLEM; MARKOV CHAIN; MARKOWITZ'S MEAN-VARIANCE PORTFOLIO SELECTION; SINGULAR PERTURBATION; SWITCHING DIFFUSION;

DISCRETE TIME CONTROL SYSTEMS;

EID: 1842482633     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2004.824479     Document Type: Article

References (32)

1. G. Barone-Adesi and R. Whaley, "Efficient analytic approximation of American option values," J. Finance, vol. 42, pp. 301-320, 1987.
2. P. Billingsley, Convergence of Probability Measures. New York: Wiley, 1968.
3. J. Buffington and R. J. Elliott, "American options with regime switching," Int. J. Theoret. Appl. Finance, vol. 5, pp. 497-514, 2002.
4. S. Chen, X. Li, and X. Y. Zhou, "Stochastic linear quadratic regulators with indefinite control weight costs," in SIAM J. Control Optim., vol. 36, 1998, pp. 1685-1702.
5. G. B. Di Masi, Y. M. Kabanov, and W. J. Runggaldier, "Mean variance hedging of options on stocks with Markov volatility," Theory Probab. Appl., vol. 39, pp. 173-181, 1994.
6. D. Duffle and H. Richardson, "Mean-variance hedging in continuous time," Ann. Appl. Probab., vol. 1, pp. 1-15, 1991.
7. E. J. Elton and M. J. Gruber, Finance as a Dynamic Process. Upper Saddle River, NJ: Prentice-Hall, 1975.
8. J. C. Francis, Investments: Analysis and Management. New York: McGraw-Hill, 1976.
9. R. R. Grauer and N. H. Hakansson, "On the use of mean-variance and quadratic approximations in implementing dynamic investment strategies: A comparison of returns and investment policies," Manage. Sci., vol. 39, pp. 856-871, 1993.
10. N. H. Hakansson, "Multi-period mean-variance analysis: Toward a general theory of portfolio choice," J. Finance, vol. 26, pp. 857-884, 1971.
11. I. Karatzas and S. E. Shreve, Methods of Mathematical Finance. New York: Springer-Verlag, 1998.
12. H. J. Kushner, Approximation and Weak Convergence Methods for Random Processes, with applications to Stochastic Systems Theory. Cambridge, MA: MIT Press, 1984.
13. D. Li and W. L. Ng, "Optimal dynamic portfolio selection: Multi-period mean-variance formulation," Math. Finance, vol. 10, pp. 387-406, 2000.
14. R. H. Liu, G. Yin, and Q. Zhang, "Asymptotically optimal controls of hybrid linear quadratic regulators in discrete time," Automatica, vol. 38, pp. 409-419, 2002.
15. D.G. Luenberger, Investment Science. New York: Oxford Univ. Press, 1998.
16. H. Markowitz, "Portfolio selection," J. Finance, vol. 7, pp.77-91, 1952.
17. _, Portfolio Selection: Efficient Diversification of Investment. New York: Wiley, 1959.
18. R. C. Merton, "An intertemporal capital asset pricing model," Econometrica, vol. 41, pp. 867-888, 1973.
19. J. Mossin, "Optimal multiperiod portfolio policies," J. Business, vol. 41, pp. 215-229, 1968.
20. S. R. Pliska, Introduction to Mathematical Finance: Discrete Time Models. Oxford, U.K.: Blackwell, 1997.
21. P. A. Samuelson, "Lifetime portfolio selection by dynamic stochastic programming," Rev. Econ. Statist., vol. 51, pp. 239-246, 1969.
22. M. Schweizer, "Approximation pricing and the variance-optinial martingale measure," Ann. Probab., vol. 24, pp. 206-236, 1996.
23. G. Yin and Q. Zhang, Continuous-Time Markov Chains and Applications: A Singular Perturbation Approach. New York: Springer-Verlag, 1998.
24. _, "Singularly perturbed discrete-time Markov chains," SIAM J. Appl. Math., vol. 61, pp. 834-854, 2000.
25. G. Yin, R. H. Liu, and Q. Zhang, "Recursive algorithms for stock Liquidation: A stochastic optimization approach," SIAM J. Optim., vol. 13, pp. 240-263, 2002.
26. G. Yin, Q. Zhang, and G. Badowski, "Asymptotic properties of a singularly perturbed Markov chain with inclusion of transient states," Ann. Appl. Probab., vol. 10, pp. 549-572, 2000.
27. _, "Discrete-time singularly perturbed Markov chains: Aggregation, occupation measures, and switching diffusion limit," Adv. Appl. Probab., vol. 35, pp. 449-476, 2003.
28. J. Yong and X. Y. Zhou, Stochastic Controls: Hamiltonian Systems and HJB Equations. New York: Springer-Verlag, 1999.
29. T. Zariphopoulou, "Investment-consumption models with transactions costs and Markov-chain parameters," SIAM J. Control Optim., vol. 30, pp. 613-636, 1992.
30. Q. Zhang, "Stock trading: An optimal selling rule," SIAM J. Control Optim., vol. 40, pp. 64-87, 2001.
31. X. Y. Zhou and D. Li, "Continuous-Time mean-variance portfolio selection: A stochastic LQ framework," Appl. Math. Optim., vol. 42, pp. 19-33, 2000.
32. X. Y. Zhou and G. Yin, "Markowitz's mean-variance portfolio selection with regime switching: A continuous-time model," SIAM J. Control Optim., vol. 42, pp. 1466-1482, 2003.