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Time consistent policy of multi-period mean-variance problem in stochastic markets
1. | Department of Computing Science, School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, Shaanxi, 710049 |
2. | Department of Computing Science, School of Mathematics and Statistics, Xi'an Jiaotong University, 710049, Xi'an, Shaanxi, China, China |
References:
[1] |
P. Artzner, F. Delbaen, J. M. Eber, D. Heath and H. Ku, Coherent multi-period risk adjusted values and Bellman's principle, Annals of Operations Research, 152 (2007), 5-22.
doi: 10.1007/s10479-006-0132-6. |
[2] |
S. Basak and G. Chabakauri, Dynamic mean-variance asset allocation, Review of Financial Studies, 23 (2010), 2970-3016.
doi: 10.1093/rfs/hhq028. |
[3] |
D. Bertsimas, G. J. Lauprete and A. Samarov, Shortfall as a risk measure: properties, optimization and app1ications, Journal of Economic Dynamics and Control, 28 (2004), 1353-1381. |
[4] |
T. Björk and A. Murgoci, A general theory of Markovian time inconsistent stochastic control problems, Working Paper, Stockolm School of Economics, 2009. Available from: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1694759. |
[5] |
T. Björk, A. Murgoci and X. Y. Zhou, Mean variance portfolio optimization with state dependent risk aversion, Mathematical Finance, 24 (2014), 1-24.
doi: 10.1111/j.1467-9965.2011.00515.x. |
[6] |
K. Boda and J. A. Filar, Time consistent dynamic risk measures, Mathematical Methods of Operations Research, 63 (2006), 169-186.
doi: 10.1007/s00186-005-0045-1. |
[7] |
M. Britten-Jones and A. Neuberger, Option prices, implied price processes, and stochastic volatility, Journal of Finance, 55 (2000), 839-866.
doi: 10.1111/0022-1082.00228. |
[8] |
U. Çakmak and S. Özekici, Portfolio optimization in stochastic markets, Mathematical Methods of Operations Research, 63 (2006), 151-168.
doi: 10.1007/s00186-005-0020-x. |
[9] |
E. Çanakoğlu and S. Özekici, Portfolio selection in stochastic markets with exponential utility functions, Annals of Operations Research, 166 (2009), 281-297.
doi: 10.1007/s10479-008-0406-2. |
[10] |
U. Çelikyurt and S. Özekici, Multiperiod portfolio optimization models in stochastic markets using the mean-variance approach, European Journal of Operational Research, 179 (2007), 186-202. |
[11] |
Z. P. Chen, G. Li and J. E. Guo, Optimal investment policy in the time consistent mean-variance formulation, Insurance: Mathematics and Economics, 52 (2013), 145-156.
doi: 10.1016/j.insmatheco.2012.11.007. |
[12] |
Z. P. Chen, G. Li and Y. G. Zhao, Time-consistent investment policies in Markovian markets: A case of mean-variance analysis, Journal of Economic Dynamic and Control, 40 (2014), 293-316.
doi: 10.1016/j.jedc.2014.01.011. |
[13] |
Z. P. Chen and J. Liu, Time consistent risk measure under two-level information structure and its application in dynamic portfolio selection, Working Paper, Xi'an Jiaotong university, 2014. Available from: http://t.cn/RhZ6Vrt. |
[14] |
Z. P. Chen and Y. Wang, Two-sided coherent risk measures and their application in realistic portfolio optimization, Journal of Banking and Finance, 32 (2008), 2667-2673.
doi: 10.1016/j.jbankfin.2008.07.004. |
[15] |
Z. P. Chen and L. Yang, Nonlinearly weighted convex risk measure and its application, Journal of Banking and Finance, 35 (2011), 1777-1793.
doi: 10.1016/j.jbankfin.2010.12.004. |
[16] |
P. Cheridito and M. Kupper, Composition of time-consistent dynamic monetary risk measures in discrete time, Journal of Theoretical and Applied Finance, 14 (2011), 137-162.
doi: 10.1142/S0219024911006292. |
[17] |
X. Y. Cui, D. Li, S. Y. Wang and S. S. Zhu, Better than dynamic mean-variance: Time inconsistency and free cash flow stream, Mathematical Finance, 22 (2012), 346-378.
doi: 10.1111/j.1467-9965.2010.00461.x. |
[18] |
C. Czichowsky, Time-consistent mean-variance portfolio selection in discrete and continuous time, Finance Stochastic, 17 (2013), 227-271.
doi: 10.1007/s00780-012-0189-9. |
[19] |
R. J. Elliott, T. K. Siu and L. Chan, On pricing barrier options with regime switching, Journal of Computational and Applied Mathematics, 256 (2014), 196-210.
doi: 10.1016/j.cam.2013.07.034. |
[20] |
L. G. Epstein and S. E. Zin, Substitution, risk aversion, and the temporal behavior of consumption and asset returns: A theoretical framework, Econometrica, 57 (1989), 937-969.
doi: 10.2307/1913778. |
[21] |
H. Geman and S. Ohana, Time-consistency in managing a commodity portfolio: A dynamic risk measure approach, Journal of Banking and Finance, 32 (2008), 1991-2005.
doi: 10.1016/j.jbankfin.2007.05.020. |
[22] |
R. Korn and H. Kraft, A stochastic control approach to portfolio problems with stochastic interest rates, SIAM Journal on Control and Optimization, 40 (2002), 1250-1269.
doi: 10.1137/S0363012900377791. |
[23] |
D. Li and W. L. Ng, Optimal dynamic portfolio selection: Multi-period mean-variance formulation, Mathematical Finance, 10 (2000), 387-406.
doi: 10.1111/1467-9965.00100. |
[24] |
X. Li, X. Y. Zhou and A. E. B. Lim, Dynamic mean-variance portfolio selection with no-shorting constraints, SIAM Journal on Control and Optimization, 40 (2002), 1540-1555.
doi: 10.1137/S0363012900378504. |
[25] |
H. J. Lüthi and J. Doege, Convex risk measures for portfolio optimization and concepts of flexibility, Mathematical Programming, 104 (2005), 541-559.
doi: 10.1007/s10107-005-0628-x. |
[26] |
F. Riedel, Dynamic coherent risk measures, Stochastic Processes and their Applications, 112 (2004), 185-200.
doi: 10.1016/j.spa.2004.03.004. |
[27] |
B. Roorda and J. M. Schumacher, Time consistency conditions for acceptability measures, with an applications to Tail Value at Risk, Insurance: Mathematics and Economics, 40 (2007), 209-230.
doi: 10.1016/j.insmatheco.2006.04.003. |
[28] |
A. Ruszczyński, Risk-averse dynamic programming for Markov decision processes, Mathematical Programming, Series B, 125 (2010), 235-261.
doi: 10.1007/s10107-010-0393-3. |
[29] |
A. Shapiro, On a time consistency concept in risk averse multistage stochastic programming, Operations Research Letters, 37 (2009), 143-147.
doi: 10.1016/j.orl.2009.02.005. |
[30] |
M. C. Steinbach, Markowitz revisited: Mean-variance models in financial portfolio analysis, SIAM Review, 43 (2001), 31-85.
doi: 10.1137/S0036144500376650. |
[31] |
T. Wang, A class of dynamic risk measure, Working Paper, University of British Columbia, 1999. Available from: http://web.cenet.org.cn/upfile/57263.pdf. |
[32] |
J. Wang and P. A. Forsyth, Continuous time mean variance asset allocation: A time-consistent strategy, European Journal of Operational Research, 209 (2011), 184-201.
doi: 10.1016/j.ejor.2010.09.038. |
[33] |
S. Z. Wei and Z. X. Ye, Multi-period optimization portfolio with bankruptcy control in stochastic market, Applied Mathematics and Computation, 186 (2007), 414-425.
doi: 10.1016/j.amc.2006.07.108. |
[34] |
L. Xu, R. M. Wang and D. J. Yao, Optimal stochastic investment games under Markov regime switching market, Journal of Industrial and Management Optimization, 10 (2014), 795-815.
doi: 10.3934/jimo.2014.10.795. |
[35] |
X. Y. Zhou and D. Li, Continuous-time mean-variance portfolio selection: A stochastic LQ framework, Applied Mathematics and Optimization, 42 (2000), 19-33.
doi: 10.1007/s002450010003. |
[36] |
S. S. Zhu, D. Li and S. Y. Wang, Risk control over bankruptcy in dynamic portfolio selection: A generalized mean-variance formulation, IEEE Transactions on Automatic Control, 49 (2004), 447-457.
doi: 10.1109/TAC.2004.824474. |
show all references
References:
[1] |
P. Artzner, F. Delbaen, J. M. Eber, D. Heath and H. Ku, Coherent multi-period risk adjusted values and Bellman's principle, Annals of Operations Research, 152 (2007), 5-22.
doi: 10.1007/s10479-006-0132-6. |
[2] |
S. Basak and G. Chabakauri, Dynamic mean-variance asset allocation, Review of Financial Studies, 23 (2010), 2970-3016.
doi: 10.1093/rfs/hhq028. |
[3] |
D. Bertsimas, G. J. Lauprete and A. Samarov, Shortfall as a risk measure: properties, optimization and app1ications, Journal of Economic Dynamics and Control, 28 (2004), 1353-1381. |
[4] |
T. Björk and A. Murgoci, A general theory of Markovian time inconsistent stochastic control problems, Working Paper, Stockolm School of Economics, 2009. Available from: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1694759. |
[5] |
T. Björk, A. Murgoci and X. Y. Zhou, Mean variance portfolio optimization with state dependent risk aversion, Mathematical Finance, 24 (2014), 1-24.
doi: 10.1111/j.1467-9965.2011.00515.x. |
[6] |
K. Boda and J. A. Filar, Time consistent dynamic risk measures, Mathematical Methods of Operations Research, 63 (2006), 169-186.
doi: 10.1007/s00186-005-0045-1. |
[7] |
M. Britten-Jones and A. Neuberger, Option prices, implied price processes, and stochastic volatility, Journal of Finance, 55 (2000), 839-866.
doi: 10.1111/0022-1082.00228. |
[8] |
U. Çakmak and S. Özekici, Portfolio optimization in stochastic markets, Mathematical Methods of Operations Research, 63 (2006), 151-168.
doi: 10.1007/s00186-005-0020-x. |
[9] |
E. Çanakoğlu and S. Özekici, Portfolio selection in stochastic markets with exponential utility functions, Annals of Operations Research, 166 (2009), 281-297.
doi: 10.1007/s10479-008-0406-2. |
[10] |
U. Çelikyurt and S. Özekici, Multiperiod portfolio optimization models in stochastic markets using the mean-variance approach, European Journal of Operational Research, 179 (2007), 186-202. |
[11] |
Z. P. Chen, G. Li and J. E. Guo, Optimal investment policy in the time consistent mean-variance formulation, Insurance: Mathematics and Economics, 52 (2013), 145-156.
doi: 10.1016/j.insmatheco.2012.11.007. |
[12] |
Z. P. Chen, G. Li and Y. G. Zhao, Time-consistent investment policies in Markovian markets: A case of mean-variance analysis, Journal of Economic Dynamic and Control, 40 (2014), 293-316.
doi: 10.1016/j.jedc.2014.01.011. |
[13] |
Z. P. Chen and J. Liu, Time consistent risk measure under two-level information structure and its application in dynamic portfolio selection, Working Paper, Xi'an Jiaotong university, 2014. Available from: http://t.cn/RhZ6Vrt. |
[14] |
Z. P. Chen and Y. Wang, Two-sided coherent risk measures and their application in realistic portfolio optimization, Journal of Banking and Finance, 32 (2008), 2667-2673.
doi: 10.1016/j.jbankfin.2008.07.004. |
[15] |
Z. P. Chen and L. Yang, Nonlinearly weighted convex risk measure and its application, Journal of Banking and Finance, 35 (2011), 1777-1793.
doi: 10.1016/j.jbankfin.2010.12.004. |
[16] |
P. Cheridito and M. Kupper, Composition of time-consistent dynamic monetary risk measures in discrete time, Journal of Theoretical and Applied Finance, 14 (2011), 137-162.
doi: 10.1142/S0219024911006292. |
[17] |
X. Y. Cui, D. Li, S. Y. Wang and S. S. Zhu, Better than dynamic mean-variance: Time inconsistency and free cash flow stream, Mathematical Finance, 22 (2012), 346-378.
doi: 10.1111/j.1467-9965.2010.00461.x. |
[18] |
C. Czichowsky, Time-consistent mean-variance portfolio selection in discrete and continuous time, Finance Stochastic, 17 (2013), 227-271.
doi: 10.1007/s00780-012-0189-9. |
[19] |
R. J. Elliott, T. K. Siu and L. Chan, On pricing barrier options with regime switching, Journal of Computational and Applied Mathematics, 256 (2014), 196-210.
doi: 10.1016/j.cam.2013.07.034. |
[20] |
L. G. Epstein and S. E. Zin, Substitution, risk aversion, and the temporal behavior of consumption and asset returns: A theoretical framework, Econometrica, 57 (1989), 937-969.
doi: 10.2307/1913778. |
[21] |
H. Geman and S. Ohana, Time-consistency in managing a commodity portfolio: A dynamic risk measure approach, Journal of Banking and Finance, 32 (2008), 1991-2005.
doi: 10.1016/j.jbankfin.2007.05.020. |
[22] |
R. Korn and H. Kraft, A stochastic control approach to portfolio problems with stochastic interest rates, SIAM Journal on Control and Optimization, 40 (2002), 1250-1269.
doi: 10.1137/S0363012900377791. |
[23] |
D. Li and W. L. Ng, Optimal dynamic portfolio selection: Multi-period mean-variance formulation, Mathematical Finance, 10 (2000), 387-406.
doi: 10.1111/1467-9965.00100. |
[24] |
X. Li, X. Y. Zhou and A. E. B. Lim, Dynamic mean-variance portfolio selection with no-shorting constraints, SIAM Journal on Control and Optimization, 40 (2002), 1540-1555.
doi: 10.1137/S0363012900378504. |
[25] |
H. J. Lüthi and J. Doege, Convex risk measures for portfolio optimization and concepts of flexibility, Mathematical Programming, 104 (2005), 541-559.
doi: 10.1007/s10107-005-0628-x. |
[26] |
F. Riedel, Dynamic coherent risk measures, Stochastic Processes and their Applications, 112 (2004), 185-200.
doi: 10.1016/j.spa.2004.03.004. |
[27] |
B. Roorda and J. M. Schumacher, Time consistency conditions for acceptability measures, with an applications to Tail Value at Risk, Insurance: Mathematics and Economics, 40 (2007), 209-230.
doi: 10.1016/j.insmatheco.2006.04.003. |
[28] |
A. Ruszczyński, Risk-averse dynamic programming for Markov decision processes, Mathematical Programming, Series B, 125 (2010), 235-261.
doi: 10.1007/s10107-010-0393-3. |
[29] |
A. Shapiro, On a time consistency concept in risk averse multistage stochastic programming, Operations Research Letters, 37 (2009), 143-147.
doi: 10.1016/j.orl.2009.02.005. |
[30] |
M. C. Steinbach, Markowitz revisited: Mean-variance models in financial portfolio analysis, SIAM Review, 43 (2001), 31-85.
doi: 10.1137/S0036144500376650. |
[31] |
T. Wang, A class of dynamic risk measure, Working Paper, University of British Columbia, 1999. Available from: http://web.cenet.org.cn/upfile/57263.pdf. |
[32] |
J. Wang and P. A. Forsyth, Continuous time mean variance asset allocation: A time-consistent strategy, European Journal of Operational Research, 209 (2011), 184-201.
doi: 10.1016/j.ejor.2010.09.038. |
[33] |
S. Z. Wei and Z. X. Ye, Multi-period optimization portfolio with bankruptcy control in stochastic market, Applied Mathematics and Computation, 186 (2007), 414-425.
doi: 10.1016/j.amc.2006.07.108. |
[34] |
L. Xu, R. M. Wang and D. J. Yao, Optimal stochastic investment games under Markov regime switching market, Journal of Industrial and Management Optimization, 10 (2014), 795-815.
doi: 10.3934/jimo.2014.10.795. |
[35] |
X. Y. Zhou and D. Li, Continuous-time mean-variance portfolio selection: A stochastic LQ framework, Applied Mathematics and Optimization, 42 (2000), 19-33.
doi: 10.1007/s002450010003. |
[36] |
S. S. Zhu, D. Li and S. Y. Wang, Risk control over bankruptcy in dynamic portfolio selection: A generalized mean-variance formulation, IEEE Transactions on Automatic Control, 49 (2004), 447-457.
doi: 10.1109/TAC.2004.824474. |
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