Continuous-time mean-risk portfolio selection
Annales de l'I.H.P. Probabilités et statistiques, Tome 41 (2005) no. 3, pp. 559-580.
@article{AIHPB_2005__41_3_559_0,
author = {Jin, Hanqing and Yan, Jia-An and Zhou, Xun Yu},
title = {Continuous-time mean-risk portfolio selection},
journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
pages = {559--580},
publisher = {Elsevier},
volume = {41},
number = {3},
year = {2005},
doi = {10.1016/j.anihpb.2004.09.009},
zbl = {02191867},
language = {en},
url = {www.numdam.org/item/AIHPB_2005__41_3_559_0/}
}
Jin, Hanqing; Yan, Jia-An; Zhou, Xun Yu. Continuous-time mean-risk portfolio selection. Annales de l'I.H.P. Probabilités et statistiques, Tome 41 (2005) no. 3, pp. 559-580. doi : 10.1016/j.anihpb.2004.09.009. http://www.numdam.org/item/AIHPB_2005__41_3_559_0/

[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. | MR 2132190 | Zbl 05004610

[2] X. Cai, K.L. Teo, X. Yang, X.Y. Zhou, Portfolio optimization under a minimax rule, Manag. Sci. 46 (2000) 957-972.

[3] J. Cvitanić, I. Karatzas, On dynamic measures of risk, Finance Stochast. 3 (1999) 451-482. | MR 1842283 | Zbl 0982.91030

[4] N. El Karoui, S. Peng, M.C. Quenez, Backward stochastic differential equations in finance, Math. Finance 7 (1997) 1-71. | MR 1434407 | Zbl 0884.90035

[5] R.J. Elliott, P.E. Kopp, Mathematics of Financial Markets, Springer-Verlag, New York, 1999. | MR 1674047 | Zbl 0943.91035

[6] P.C. Fishburn, Mean-risk analysis with risk associated with below-target returns, Amer. Econ. Rev. 67 (1977) 116-126.

[7] H. Föllmer, P. Leukert, Quantile hedging, Finance Stochast. 3 (1999) 251-273. | MR 1842286 | Zbl 0977.91019

[8] H. Jin, X.Y. Zhou, Continuous-time Markowitz's problems in an incomplete market, with constrained portfolios, Working paper, 2004.

[9] P. Jorion, Vale at Risk: The New Benchmark for Managing Financial Risk, McGraw-Hill, New York, 2001.

[10] I. Karatzas, S.E. Shreve, Methods of Mathematical Finance, Springer-Verlag, New York, 1998. | MR 1640352 | Zbl 0941.91032

[11] M. Kulldorff, Optimal control of a favorable game with a time-limit, SIAM J. Contr. Optim. 31 (1993) 52-69. | MR 1200222 | Zbl 0770.90099

[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] 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. | MR 1882807 | Zbl 1027.91040

[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. | MR 1886222 | Zbl 1082.91521

[15] J. Ma, P. Protter, J. Yong, Solving forward-backward stochastic differential equations explicitly - a four step scheme, Prob. Theory Related Fields 98 (1994) 339-359. | MR 1262970 | Zbl 0794.60056

[16] J. Ma, J. Yong, Forward-Backward Stochastic Differential Equations and Their Applications, Lect. Notes in Math., vol. 1702, Springer-Verlag, New York, 1999. | MR 1704232 | Zbl 0927.60004

[17] H. Markowitz, Portfolio selection, J. Finance 7 (1952) 77-91.

[18] H. Markowitz, Portfolio Selection: Efficient Diversification of Investments, Wiley, New York, 1959. | MR 103768

[19] D. Nawrocki, A brief history of downside risk measures, J. Investing 8 (1999) 9-25.

[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. | MR 794525 | Zbl 0501.90088

[21] R.T. Rockafellar, Convex Analysis, Princeton University Press, Princeton, 1970. | MR 274683 | Zbl 0193.18401

[22] F.A. Sortino, R. Van Der Meer, Downside risk, J. Portfolio Manag. 17 (1991) 27-31.

[23] M.C. Steinbach, Markowitz revisited: mean-variance models in financial portfolio analysis, SIAM Rev. 43 (2001) 31-85. | MR 1854646 | Zbl 1049.91086

[24] J. Yong, X.Y. Zhou, Stochastic Controls: Hamiltonian Systems and HJB Equations, Springer, New York, 1999. | MR 1696772 | Zbl 0943.93002

[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. | MR 1963526 | Zbl 1050.91055

[26] X.Y. Zhou, D. Li, Continuous time mean-variance portfolio selection: a stochastic LQ framework, Appl. Math. Optim. 42 (2000) 19-33. | MR 1751306 | Zbl 0998.91023