Optimal multi-period mean-variance policy under no-shorting constraint. (English) Zbl 1304.91185

Summary: We consider in this paper the mean-variance formulation in multi-period portfolio selection under no-shorting constraint. Recognizing the structure of a piecewise quadratic value function, we prove that the optimal portfolio policy is piecewise linear with respect to the current wealth level, and derive the semi-analytical expression of the piecewise quadratic value function. One prominent feature of our findings is the identification of a deterministic time-varying threshold for the wealth process and its implications for market settings. We also generalize our results in the mean-variance formulation to utility maximization with no-shorting constraint.


91G10 Portfolio theory
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[1] Bertsekas, D. P., Dynamic Programming and Optimal Control, vol. 1, (2001), Athena Scientific · Zbl 1083.90044
[2] Bielecki, T.; Jin, H.; Pliska, S.; Zhou, X. Y., Continuous-time mean-variance portfolio selection with bankruptcy prohibition, Math. Finance, 15, 213-244, (2005) · Zbl 1153.91466
[3] Chiu, M. C.; Wong, H. Y., Mean-variance asset-liability management: cointegrated assets and insurance liability, Euro. J. Oper. Res., 223, 785-793, (2012) · Zbl 1292.91158
[4] Cui, X. Y.; Li, D.; Wang, S. Y.; Zhu, S. S., Better than dynamic mean-variance: time inconsistency and free cash flow stream, Math. Finance, 22, 346-378, (2012) · Zbl 1278.91131
[5] Cvitanić, J.; Karatzas, I., Convex duality in constrained portfolio optimization, Ann. Appl. Probab., 2, 767-818, (1992) · Zbl 0770.90002
[6] Czichowsky, C., Schweizer, M., 2010. Convex Duality in Mean-Variance Hedging Under Convex Trading Constraints, NCCR FINRISK working paper No. 667, ETH Zurich.
[7] Czichowsky, C., Schweizer, M., 2011. Cone-Constrained Continuous-Time Markowitz Problems, NCCR FINRISK working paper No. 683, ETH Zurich.
[8] Fu, C.; Lari-Lavassani, A.; Li, X., Dynamic meancvariance portfolio selection with borrowing constraint, Euro. J. Oper. Res., 200, 312C319, (2010)
[9] Gao, J.J., Li, D., Cui, X.Y., Wang, S.Y., 2012. Market timing strategy in dynamic portfolio selection: a mean-variance formulation. http://papers.ssrn.com/sol3/papers.cfm?abstractid=2015580.
[10] Gulpinar, N.; Rustem, B., Worst-case robust decisions for multi-period mean-variance portfolio optimization, Euro. J. Oper. Res., 183, 981-1000, (2007) · Zbl 1138.91446
[11] Labbé, C.; Heunis, A. J., Convex duality in constrained mean-variance portfolio optimization, Adv. Appl. Probab., 39, 77-104, (2007) · Zbl 1110.93051
[12] Li, D.; Ng, W. L., Optimal dynamic portfolio selection: multiperiod mean-variance formulation, Math. Finance, 10, 387-406, (2000) · Zbl 0997.91027
[13] Li, X.; Zhou, X. Y.; Lim, A. E.B., Dynamic mean-variance portfolio selection with no-shorting constraints, SIAM J. Control Optim., 40, 1540-1555, (2002) · Zbl 1027.91040
[14] Li, X.; Qin, Z.; Kar, S., Mean-variance-skewness model for portfolio selection with fuzzy returns, Euro. J. Oper. Res., 202, 239-247, (2010) · Zbl 1175.90438
[15] Markowitz, H. M., Portfolio selection, J. Finance, 7, 77-91, (1952)
[16] Markowitz, H. M., The optimization of a quadratic function subject to linear constraints, Nav. Res. Log., 3, 111-133, (1956)
[17] Markowitz, H.M., 2000. Personal Communication with Duan Li. The Chinese University of Hong Kong.
[18] Merton, R. C., An analytical derivation of the efficient portfolio frontier, J. Finance Quant. Anal., 7, 1851-1872, (1972)
[19] Pliska, S. R., Introduction to mathematical finance, (1997), Basil Blackwell Malden, MA
[20] Sun, W. G.; Wang, C. F., The mean-variance investment problem in a constrained financial market, J. Math. Econ., 42, 885-895, (2006) · Zbl 1153.91565
[21] Wang, J.; Forsyth, P. A., Continuous time mean variance asset allocation: a time-consistent strategy, Euro. J. Oper. Res., 209, 184-201, (2011) · Zbl 1208.91139
[22] Xu, G. L.; Shreve, S. E., A duality method for optimal consumption and investment under short-selling prohibition: I. general market coefficients, Ann. Appl. Probab., 2, 87-112, (1992) · Zbl 0745.93083
[23] Xu, G. L.; Shreve, S. E., A duality method for optimal consumption and investment under short-selling prohibition: II. constant market coefficients, Ann. Appl. Probab., 2, 314-328, (1992) · Zbl 0773.90017
[24] Zhou, X. Y.; Li, D., Continuous time mean-variance portfolio selection: a stochastic LQ framework, Appl. Math. Optim., 42, 19-33, (2000) · Zbl 0998.91023
[25] Zhu, S. S.; Li, D.; Wang, S. Y., Risk control over bankruptcy in dynamic portfolio selection: a generalized mean-variance formulation, IEEE Trans. Automat. Contr., 49, 447-457, (2004) · Zbl 1366.91150
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