Continuous-time mean–risk portfolio selection

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1. [1] T.R. Bielecki, S.R. Pliska, H. Jin, X.Y. Zhou, Continuous-time mean–variance portfolio selection with bankruptcy prohibition, Math. Finance, in press. Zbl1153.91466MR2132190
2. [2] X. Cai, K.L. Teo, X. Yang, X.Y. Zhou, Portfolio optimization under a minimax rule, Manag. Sci.46 (2000) 957-972. Zbl1231.91149
3. [3] J. Cvitanić, I. Karatzas, On dynamic measures of risk, Finance Stochast.3 (1999) 451-482. Zbl0982.91030MR1842283
4. [4] N. El Karoui, S. Peng, M.C. Quenez, Backward stochastic differential equations in finance, Math. Finance7 (1997) 1-71. Zbl0884.90035MR1434407
5. [5] R.J. Elliott, P.E. Kopp, Mathematics of Financial Markets, Springer-Verlag, New York, 1999. Zbl0943.91035MR1674047
6. [6] P.C. Fishburn, Mean-risk analysis with risk associated with below-target returns, Amer. Econ. Rev.67 (1977) 116-126. 
7. [7] H. Föllmer, P. Leukert, Quantile hedging, Finance Stochast.3 (1999) 251-273. Zbl0977.91019MR1842286
8. [8] H. Jin, X.Y. Zhou, Continuous-time Markowitz's problems in an incomplete market, with constrained portfolios, Working paper, 2004. 
9. [9] P. Jorion, Vale at Risk: The New Benchmark for Managing Financial Risk, McGraw-Hill, New York, 2001. 
10. [10] I. Karatzas, S.E. Shreve, Methods of Mathematical Finance, Springer-Verlag, New York, 1998. Zbl0941.91032MR1640352
11. [11] M. Kulldorff, Optimal control of a favorable game with a time-limit, SIAM J. Contr. Optim.31 (1993) 52-69. Zbl0770.90099MR1200222
12. [12] H. Konno, H. Yamazaki, Mean–absolute deviation portfolio optimization model and its application to Tokyo stock market, Manag. Sci.37 (1991) 519-531. 
13. [13] X. Li, X.Y. Zhou, A.E.B. Lim, Dynamic mean–variance portfolio selection with no-shorting constraints, SIAM J. Contr. Optim.40 (2001) 1540-1555. Zbl1027.91040MR1882807
14. [14] A.E.B. Lim, X.Y. Zhou, Mean–variance portfolio selection with random parameters in a complete market, Math. Oper. Res.27 (2002) 101-120. Zbl1082.91521MR1886222
15. [15] J. Ma, P. Protter, J. Yong, Solving forward–backward stochastic differential equations explicitly – a four step scheme, Prob. Theory Related Fields98 (1994) 339-359. Zbl0794.60056MR1262970
16. [16] J. Ma, J. Yong, Forward–Backward Stochastic Differential Equations and Their Applications, Lect. Notes in Math., vol. 1702, Springer-Verlag, New York, 1999. Zbl0927.60004MR1704232
17. [17] H. Markowitz, Portfolio selection, J. Finance7 (1952) 77-91. 
18. [18] H. Markowitz, Portfolio Selection: Efficient Diversification of Investments, Wiley, New York, 1959. MR103768
19. [19] D. Nawrocki, A brief history of downside risk measures, J. Investing8 (1999) 9-25. 
20. [20] S.R. Pliska, A discrete time stochastic decision model, in: Fleming W.H., Gorostiza L.G. (Eds.), Advances in Filtering and Optimal Stochastic Control, Lecture Notes in Control and Information Sci., vol. 42, Springer-Verlag, New York, 1982, pp. 290-304. Zbl0501.90088MR794525
21. [21] R.T. Rockafellar, Convex Analysis, Princeton University Press, Princeton, 1970. Zbl0193.18401MR274683
22. [22] F.A. Sortino, R. van der Meer, Downside risk, J. Portfolio Manag.17 (1991) 27-31. 
23. [23] M.C. Steinbach, Markowitz revisited: mean–variance models in financial portfolio analysis, SIAM Rev.43 (2001) 31-85. Zbl1049.91086MR1854646
24. [24] J. Yong, X.Y. Zhou, Stochastic Controls: Hamiltonian Systems and HJB Equations, Springer, New York, 1999. Zbl0943.93002MR1696772
25. [25] X.Y. Zhou, Markowitz's world in continuous-time, and beyond, in: Yao D.D., (Eds.), Stochastic Modeling and Optimization, Springer, New York, 2003, pp. 279-310. Zbl1050.91055MR1963526
26. [26] X.Y. Zhou, D. Li, Continuous time mean–variance portfolio selection: a stochastic LQ framework, Appl. Math. Optim.42 (2000) 19-33. Zbl0998.91023MR1751306