Continuous-time mean-variance portfolio selection with bankruptcy prohibition

Mathematical Finance

Volumn 15, Issue 2, 2005, Pages 213-244

  Bielecki, Tomasz R ^a   Jin, Hanqing ^b   Pliska, Stanley R ^c   Zhou, Xun Yu ^b  

^a ILLINOIS INSTITUTE OF TECHNOLOGY   (United States)

^b CHINESE UNIVERSITY OF HONG KONG   (Hong Kong)

^c UNIVERSITY OF ILLINOIS AT CHICAGO   (United States)

Author keywords

Backward stochastic differential equation; Black Scholes equation; Contingent claim; Continuous time; Lagrange multiplier; Mean variance portfolio selection

Indexed keywords

EID: 17444409678     PISSN: 09601627     EISSN: None     Source Type: Journal    
DOI: 10.1111/j.0960-1627.2005.00218.x     Document Type: Article

References (33)

1. CVITANIC, J., and I. KARATZAS (1992): Convex Duality in Constrained Portfolio Optimization, Ann. Appl. Prob. 2, 767-818.
2. DUFFIE, D., and H. R. RICHARDSON (1991): Mean Variance Hedging in Continuous Time, Ann. Appl. Prob, 1, 1-15.
3. EL KAROUI, N., S. PENG, and M. C. QUENEZ (1997): Backward Stochastic Differential Equations in Finance, Math. Finance 1, 1-71.
4. ELLIOTT, R. J., and R E. KOPP (1999): Mathematics of Financial Markets. New York: Springer-Verlag.
5. GRAUER, R. R., and N. H. HAKANSSON (1993): On the Use of Mean-Variance and Quadratic Approximations in Implementing Dynamic Investment Strategies: A Comparison of the Returns and Investment Policies, Mgmt. Sci. 39, 856-871.
6. HAKANSSON, N. H. (1971): Capital Growth and the Mean-Variance Approach to Portfolio Management, J. Financial Quant. Anal. 6, 517-557.
7. KARATZAS, I., and S. E. SHREVE (1998): Methods of Mathematical Finance. New York: Springer-Verlag.
8. KOHLMANN, M., and X. Y. ZHOU (2000): Relationship between Backward Stochastic Differential Equations and Stochastic Controls: A Linear-Quadratic Approach, SIAM J. Control Optim. 38, 1392-1407.
9. KORN, R. (1997): Optimal Portfolios. Singapore: World Scientific.
10. KORN, R., and S. TRAUTMANN (1995): Continuous-Time Portfolio Optimization under Terminal Wealth Constraints, ZOR 42, 69-93.
11. LI, D., and W. L. NG (2000): Optimal Dynamic Portfolio Selection: Multiperiod Mean-Variance Formulation, Math. Finance 10, 387-406.
12. LI, X., X. Y. ZHOU, and A. E. B. LIM (2001): Dynamic Mean-Variance Portfolio Selection with No-Shorting Constraints, SIAM J. Control Optim. 40, 1540-1555.
13. LIM, A. E. B., and X. Y. ZHOU (2002): Mean-Variance Portfolio Selection with Random Parameters, Math. Oper. Res. 27, 101-120.
14. LINTNER, J. (1965): The Valuation of Risk Assets and the Selection of Risky Investment in Stock Portfolios and Capital Budgets, Rev. Econ. Stat. 47, 13-37.
15. MA, J., P. PROTTER, and J. YONG (1994): Solving Forward-Backward Stochastic Differential Equations Explicitly-A Four Step Scheme, Prob. Theory & Rel. Fields 98, 339-359.
16. MA, J., and J. YONG (1999): Forward-Backward Stochastic Differential Equations and Their Applications, Lect. Notes Math. 1702. Berlin: Springer-Verlag.
17. MARKOWITZ, H. (1952): Portfolio Selection, J. of Finance 7, 77-91.
18. MARKOWITZ, H. (1959): Portfolio Selection: Efficient Diversification of Investments, New York: Wiley.
19. MARKOWITZ, H. (1987): Mean-Variance Analysis in Portfolio Choice and Capital Markets, New Hope, PA: Frank J. Fabozzi Associates.
20. MERTON, R. (1971, 1973): Optimum Consumption and Portfolio Rules in a Continuous Time Model, J. Econ. Theory 3, 373-413; Erratum, J. Econ. Theory 6, 213-214.
21. MOSSIN, J. (1966): Equilibrium in a Capital Asset Market, Econometrica 34, 768-783.
22. PLISKA, S. R. (1982): A Discrete Time Stochastic Decision Model; in Advances in Filtering and Optimal Stochastic Control 42, W. H. FLEMING and L. G. GOROSTIZA, eds., Lecture Notes in Control and Information Sciences. New York: Springer-Verlag, 290-302.
23. PLISKA, S. R. (1986): A Stochastic Calculus Model of Continuous Trading: Optimal Portfolios, Math. Oper. Res. 11, 371-384.
24. PLISKA, S. R. (1997): Introduction to Mathematical Finance. Oxford: Blackwell.
25. RICHARDSON, H. R. (1989): A Minimum Variance Result in Continuous Trading Portfolio Optimization, Mgmt. Sci. 35, 1045-1055.
26. SAMUELSON, P. A. (1986): Lifetime Portfolio Selection by Dynamic Stochastic Programming, Rev. Econ. Stat. 51, 371-382.
27. SCHWEIZER, M. (1992): Mean-Variance Hedging for General Claims, Ann. Appl. Prob. 2, 171-179.
28. SHARPE, W. F. (1964): Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk, J. of Finance 19, 425-442.
29. YONG, J., and X. Y. ZHOU (1999): Stochastic Controls: Hamiltonian Systems and HJB Equations. New York: Springer.
30. ZHAO, Y, and W. T. ZIEMBA (2000): Mean-Variance versus Expected utility in Dynamic Investment Analysis. Working paper, Faculty of Commerce and Business Administration, University of British Columbia.
31. ZHOU, X. Y. (2003): Markowitz's World in Continuous Time, and Beyond; in Stochastic Modeling and Optimization, D. D. YAO, H. Zhang, and X. Y. Zhou, eds. New York: Springer, 279-310.
32. ZHOU, X. Y., and D. LI (2000): Continuous Time Mean-Variance Portfolio Selection: A Stochastic LQ Framework, Appl. Math. Optim. 42, 19-33.
33. ZHOU, X. Y., and G. YIN (2003): Markowitz's Mean-Variance Portfolio Selection with Regime Switching: A Continuous Time Model, SIAM J. Control Optim. 42, 1466-1482.