Markowitz's mean-variance portfolio selection with regime switching: A continuous-time model

SIAM Journal on Control and Optimization

Volumn 42, Issue 4, 2003, Pages 1466-1482

  Zhou, Xun Yu ^a   Yin, G ^b  

^a CHINESE UNIVERSITY OF HONG KONG   (Hong Kong)

^b WAYNE STATE UNIVERSITY   (United States)

Author keywords

Continuous time; Efficient frontier; Linear quadratic control; Markov chain; Mean variance; Portfolio selection; Regime switching

Indexed keywords

CONTINUOUS TIME; PORTFOLIO SELECTION; REGIME SWITCHING; STOCHASTIC DIFFERENTIAL EQUATIONS (SDE);

BROWNIAN MOVEMENT; DIFFERENTIAL EQUATIONS; MARKOV PROCESSES; MATHEMATICAL MODELS; PARAMETER ESTIMATION; PERTURBATION TECHNIQUES; STOCHASTIC CONTROL SYSTEMS; THEOREM PROVING;

LINEAR CONTROL SYSTEMS;

EID: 1842451084     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0363012902405583     Document Type: Article

References (31)

1. G. BARONE-ADESI AND R. WHALEY, Efficient analytic approximation of American option values, J. Fin., 42 (1987), pp. 301-320.
2. T. BJÖRK, Finite dimensional optimal filters for a class of Itô-processes with jumping parameters, Stochastics, 4 (1980/1981), pp. 167-183.
3. J. BUFFINGTON AND R. ELLIOTT, American options with regime switching, Int. J. Theor. Appl. Finance, 5 (2002), pp. 497-514.
4. S. CHEN, X, LI, AND X. Y. ZHOU, Stochastic linear quadratic regulators with indefinite control weight costs, SIAM J. Control Optim., 36 (1998), pp. 1685-1702.
5. S. CHEN AND X. Y. ZHOU, Stochastic linear quadratic regulators with indefinite control weight costs II, SIAM J. Control Optim., 39 (2000), pp. 1065-1081.
6. G. B. DI MASI, Y. M. KABANOV, AND W. J. RUNGGALDIER, Mean variance hedging of options on stocks with Markov volatility, Theory Probab. Appl., 39 (1994), pp. 173-181.
7. D. DUFFIE AND H. RICHARDSON, Mean-variance hedging in continuous time, Ann. Appl. Probab., 1 (1991), pp. 1-15.
8. R. J. ELLIOTT, W. P. MALCOLM, AND A. TSOI, Robust parameter estimation for asset price models with Markov modulated volatilities, J. Econom. Dynam. Control, 27 (2003), pp. 1391-1409.
9. W. H. FLEMING AND H. M. SONER, Controlled Markov Processes and Viscosity Solutions, Springer-Verlag, New York, 1993.
10. X. GUO, Insider Information and Stock Fluctuations, Ph.D. thesis, Rutgers University, New Brunswick, NJ, 1999.
11. N. H. HAKANSSON, Multi-period mean-variance analysis: Toward a general theory of portfolio choice, J. Fin., 26 (1971), pp. 857-884.
12. M. KOHLMANN AND X. Y. ZHOU, Relationship between backward stochastic differential equations and stochastic controls: A linear-quadratic approach, SIAM J. Control Optim., 38 (2000), pp. 1392-1407.
13. R. KORN, Optimal Portfolios - Stochastic Models for Optimal Investment and Risk Management in Continuous Time, World Scientific, Singapore, 1997.
14. R. KORN AND S. TRAUTMANN, Continuous-time portfolio optimization under terminal wealth constraints, ZOR - Math. Methods Oper. Res., 42 (1995), pp. 69-92.
15. X. Li, X. Y. ZHOU, AND A. E. B. LIM, Dynamic mean-variance portfolio selection with no-shorting constraints, SIAM J. Control Optim., 40 (2002), pp. 1540-1555.
16. A. E. B. LIM AND X. Y. ZHOU, Mean-variance portfolio selection with random coefficients in a complete market, Math. Oper. Res., 27 (2002), pp. 101-120.
17. D. G. LUENBERGER, Optimization by Vector Space Methods, John Wiley, New York, 1968.
18. D. G. LUENBERGER, Investment Science, Oxford University Press, New York, 1998.
19. D. LI AND W. L. NG, Optimal dynamic portfolio selection: Multi-period mean-variance formulation, Math. Finance, 10 (2000), pp. 387-406.
20. H. MARKOWITZ, Portfolio selection, J. Fin., 7 (1952), pp. 77-91.
21. H. MARKOWITZ, Portfolio Selection: Efficient Diversification of Investment, John Wiley and Sons, New York, 1959.
22. S. R. PLISKA, Introduction to Mathematical Finance, Basil Blackwell, Malden, UK, 1997.
23. P. A. SAMUELSON, Lifetime portfolio selection by dynamic stochastic programming, Rev. Econ. Statist., 51 (1969), pp. 239-246.
24. M. SCHWEIZER, Approximation pricing and the variance-optimal martingale measure, Ann. Probab., 24 (1996), pp. 206-236.
25. H. M. SONER AND N. TOUZI, Superreplication under gamma constraints, SIAM J. Control Optim., 39 (2000), pp. 73-96.
26. D. D. YAO, Q. ZHANG, AND X. Y. ZHOU, Option Pricing with Markov-Modulated Volatility, preprint, The Chinese University of Hong Kong, Hong Kong, 2001.
27. G. YIN, R. H. Liu, AND Q. ZHANG, Recursive algorithms for stock liquidation: A stochastic optimization approach, SIAM J. Optim., 13 (2002), pp. 240-263.
28. G. YIN, Q. ZHANG, AND K. YIN, Constrained stochastic estimation algorithms for a class of hybrid stock market models, J. Optim. Theory Appl., 118 (2003), pp. 157-182.
29. J. YONG AND X. Y. ZHOU, Stochastic Controls: Hamiltonian Systems and HJB Equations, Springer-Verlag, New York, 1999.
30. Q. ZHANG, Stock trading: An optimal selling rule, SIAM J. Control Optim., 40 (2001), pp. 64-87.
31. X. Y. ZHOU AND D. Li, Continuous-time mean-variance portfolio selection: A stochastic LQ framework, Appl. Math. Optim., 42 (2000), pp. 19-33.