In this paper, we deal with multi-period mean-variance portfolio selection problems with an exogenous uncertain exit-time in a regime-switching market. The market is modelled by a non-homogeneous Markov chain in which the random returns of assets depend on the states of the market and investment time periods. Applying the Lagrange duality method, we derive explicit closed-form expressions for the optimal investment strategies and the efficient frontier. Also, we show that some known results in the literature can be obtained as special cases of our results. A numerical example is provided to illustrate the results.
Accepté le :
DOI : 10.1051/ro/2018050
Mots-clés : Multi-period mean-variance portfolio selection, regime-switching, uncertain exit-time, Lagrange duality theorem, dynamic programming
@article{RO_2019__53_4_1171_0,
author = {Keykhaei, Reza},
title = {Mean-variance portfolio selection with an uncertain exit-time in a regime-switching market},
journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
pages = {1171--1186},
publisher = {EDP-Sciences},
volume = {53},
number = {4},
year = {2019},
doi = {10.1051/ro/2018050},
mrnumber = {3986365},
zbl = {1461.90163},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/ro/2018050/}
}
TY - JOUR AU - Keykhaei, Reza TI - Mean-variance portfolio selection with an uncertain exit-time in a regime-switching market JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2019 SP - 1171 EP - 1186 VL - 53 IS - 4 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ro/2018050/ DO - 10.1051/ro/2018050 LA - en ID - RO_2019__53_4_1171_0 ER -
%0 Journal Article %A Keykhaei, Reza %T Mean-variance portfolio selection with an uncertain exit-time in a regime-switching market %J RAIRO - Operations Research - Recherche Opérationnelle %D 2019 %P 1171-1186 %V 53 %N 4 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/ro/2018050/ %R 10.1051/ro/2018050 %G en %F RO_2019__53_4_1171_0
Keykhaei, Reza. Mean-variance portfolio selection with an uncertain exit-time in a regime-switching market. RAIRO - Operations Research - Recherche Opérationnelle, Tome 53 (2019) no. 4, pp. 1171-1186. doi : 10.1051/ro/2018050. http://archive.numdam.org/articles/10.1051/ro/2018050/
[1] and , Optimal mean-variance problem with constrained controls in a jump-diffusion financial market for an insurer. J. Optim. Theory Appl. 157 (2013) 252–275. | DOI | MR | Zbl
[2] , and , Dynamic mean-variance and optimal reinsurance problems under the no-bankruptcy constraint for an insurer. Ann. Oper. Res. 212 (2014) 43–59. | DOI | MR | Zbl
[3] , and , Optimal investment decisions when time-horizon is uncertain. J. Math. Econ. 44 (2008) 1100–1113. | DOI | MR | Zbl
[4] and , Portfolio optimization in stochastic markets. Math. Method. Oper. Res. 63 (2006) 151–168. | DOI | MR | Zbl
[5] , , and , Optimal multi-period mean-variance policy under no- shorting constraint. European J. Oper. Res. 234 (2014) 459–468. | DOI | MR | Zbl
[6] and , Multi-period portfolio optimization when exit-time is uncertain. J. Manag. Sci. China 8 (2005) 14–19.
[7] and , Portfolio optimization with uncertain exit time in infinite-time horizon. Acta Math. Appl. Sin. Engl. Ser. 29 (2013) 673–684. | DOI | MR | Zbl
[8] , Optimal investment and consumption strategies under risk, an uncertain lifetime, and insurance. Int. Econ. Rev. 10 (1969) 443–466. | DOI | Zbl
[9] , Optimal entrepreuneurial decisions in a completely stochastic environment. Manag. Sci. 17 (1971) 427–449. | DOI | MR | Zbl
[10] and , Utility maximization with discretionary stopping. SIAM J. Control Optim. 39 (2001) 306–329. | DOI | MR | Zbl
[11] , Mean-variance portfolio optimization when each asset has individual uncertain exit-time. Pak. J. Stat. Oper. Res. 12 (2016) 765–773. | DOI | MR | Zbl
[12] and , Optimal dynamic portfolio selection: Multiperiod mean-variance formulation. Math. Finance 10 (2000) 387–406. | DOI | MR | Zbl
[13] , and , Dynamic mean-variance portfolio selection with no-shorting constraints. SIAM J. Control Optim. 40 (2002) 1540–1555. | DOI | MR | Zbl
[14] and , Mean-variance portfolio selection with random parameters in a complete market. Math. Oper. Res. 27 (2002) 101–120. | DOI | MR | Zbl
[15] and , Optimal portfolio selection with transaction costs and finite horizons. Rev. Financial Stud. 15 (2002) 805–835. | DOI
[16] , Optimization by Vector Space Methods. Wiley, New York (1968). | MR | Zbl
[17] , and , Continuous-time mean-variance portfolio selection with random horizon in an incomplete market. Automatica 69 (2016) 176–180. | DOI | MR | Zbl
[18] , Portfolio selection. J. Finance 7 (1952) 77–91.
[19] and , Static mean variance analysis with uncertain time-horizon. Manag. Sci. 52 (2005) 955–964. | DOI
[20] , Optimal consumption and portfolio rules in a continuous-time model. J. Econ. Theory 3 (1971) 373–413. | DOI | MR | Zbl
[21] , An analytic derivation of the efficient portfolio. J. Finan. Quant. Anal. 7 (1972) 1852–1872. | DOI
[22] , Mean-variance portfolio selection with a stochastic cash flow in a Markov-switching jump-diffusion market. J. Optim. Theory Appl. 158 (2013) 918–934. | DOI | MR | Zbl
[23] and , Multi-period mean-variance portfolio selection with Markov regime switching and uncertain time-horizon. J. Syst. Sci. Complex. 24 (2011) 140–155. | DOI | MR | Zbl
[24] and , Multi-period mean-variance portfolio selection in a regime-switching market with a bankruptcy state. Optim. Control Appl. Met. 34 (2013) 415–432. | DOI | MR | Zbl
[25] , and , Multi-period Markowitz’s mean-variance portfolio selection with state-dependent exit probability. Econ. Model. 36 (2014) 69–78. | DOI
[26] , Uncertain lifetime, life insurance, and the theory of the consumer. Rev. Econ. Stud. 32 (1965) 137–150. | DOI
[27] , A simple method for solving multiperiod mean-variance asset-liability management problem. Procedia Eng. 23 (2011) 387–391. | DOI
[28] , and , Uncertain exit time multi-period mean-variance portfolio selection with endogenous liabilities and Markov jumps. Automatica 49 (2013) 3258–3269. | DOI | MR | Zbl
[29] , , and , Asset allocation for a DC pension fund with stochastic income and mortality risk: A multi-period mean-variance framework. Insur. Math. Econ. 54 (2014) 84–92. | DOI | MR | Zbl
[30] , and , Continuous-time mean-variance portfolio selection with only risky assets. Econ. Model. 36 (2014) 244–251. | DOI
[31] , and , Multi-period mean-variance asset-liability management with uncontrolled cash flow and uncertain time-horizon. Econ. Model. 30 (2013) 492–500. | DOI
[32] , , and , Multi-period mean-variance model with uncertain exit time. In Vol. 2 of 2010 Int. Conference on Information Management, Innovation Management and Industrial Engineering (ICIII). (2010) 43–46.
[33] , and , Multi-period portfolio selection for asset-liability management with uncertain investment horizon. J. Ind. Manag. Optim. 4 (2008) 535–552. | DOI | MR | Zbl
[34] and , Markowitz’s mean-variance portfolio selection with regime switching: from discrete-time models to their continuous-time limits. IEEE Trans. Autom. Control 49 (2004) 349–360. | DOI | MR | Zbl
[35] , Continuous-time mean-variance portfolio selection with random horizon. Appl. Math. Opt. 68 (2013) 333–359. | DOI | MR | Zbl
[36] and , Multi-period mean-variance portfolio selection with uncertain time horizon when returns are serially correlated. Math. Probl. Eng. 2012 (2012) 1–17. | MR | Zbl
[37] , and , Optimal portfolio selection in a Levy market with uncontrolled cash flow and only risky assets. Int. J. Control 86 (2013) 426–437. | DOI | MR | Zbl
[38] and , Continuous-time mean-variance portfolio selection: a stochastic LQ framework. Appl. Math. Opt. 42 (2000) 19–33. | DOI | MR | Zbl
[39] and , Markowitz’s mean-variance portfolio selection with regime switching: A continuous-time model. SIAM J. Control Optim. 42 (2003) 1466–1482. | DOI | MR | Zbl
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