-
Previous Article
A novel discriminant minimum class locality preserving canonical correlation analysis and its applications
- JIMO Home
- This Issue
-
Next Article
A new approach for allocating fixed costs among decision making units
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.
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.
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. Google Scholar |
[4] |
T. Björk and A. Murgoci, A general theory of Markovian time inconsistent stochastic control problems,, Working Paper, (2009). Google Scholar |
[5] |
T. Björk, A. Murgoci and X. Y. Zhou, Mean variance portfolio optimization with state dependent risk aversion,, Mathematical Finance, 24 (2014), 1.
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.
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.
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.
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.
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. Google Scholar |
[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.
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.
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, (2014). Google Scholar |
[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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
doi: 10.1007/s10107-005-0628-x. |
[26] |
F. Riedel, Dynamic coherent risk measures,, Stochastic Processes and their Applications, 112 (2004), 185.
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.
doi: 10.1016/j.insmatheco.2006.04.003. |
[28] |
A. Ruszczyński, Risk-averse dynamic programming for Markov decision processes,, Mathematical Programming, 125 (2010), 235.
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.
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.
doi: 10.1137/S0036144500376650. |
[31] |
T. Wang, A class of dynamic risk measure,, Working Paper, (1999). Google Scholar |
[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.
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.
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.
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.
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.
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.
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.
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. Google Scholar |
[4] |
T. Björk and A. Murgoci, A general theory of Markovian time inconsistent stochastic control problems,, Working Paper, (2009). Google Scholar |
[5] |
T. Björk, A. Murgoci and X. Y. Zhou, Mean variance portfolio optimization with state dependent risk aversion,, Mathematical Finance, 24 (2014), 1.
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.
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.
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.
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.
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. Google Scholar |
[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.
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.
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, (2014). Google Scholar |
[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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
doi: 10.1007/s10107-005-0628-x. |
[26] |
F. Riedel, Dynamic coherent risk measures,, Stochastic Processes and their Applications, 112 (2004), 185.
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.
doi: 10.1016/j.insmatheco.2006.04.003. |
[28] |
A. Ruszczyński, Risk-averse dynamic programming for Markov decision processes,, Mathematical Programming, 125 (2010), 235.
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.
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.
doi: 10.1137/S0036144500376650. |
[31] |
T. Wang, A class of dynamic risk measure,, Working Paper, (1999). Google Scholar |
[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.
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.
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.
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.
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.
doi: 10.1109/TAC.2004.824474. |
[1] |
Jiannan Zhang, Ping Chen, Zhuo Jin, Shuanming Li. Open-loop equilibrium strategy for mean-variance portfolio selection: A log-return model. Journal of Industrial & Management Optimization, 2021, 17 (2) : 765-777. doi: 10.3934/jimo.2019133 |
[2] |
Giuseppe Capobianco, Tom Winandy, Simon R. Eugster. The principle of virtual work and Hamilton's principle on Galilean manifolds. Journal of Geometric Mechanics, 2021 doi: 10.3934/jgm.2021002 |
[3] |
Philipp Harms. Strong convergence rates for markovian representations of fractional processes. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2020367 |
[4] |
Yiling Chen, Baojun Bian. Optimal dividend policy in an insurance company with contagious arrivals of claims. Mathematical Control & Related Fields, 2021, 11 (1) : 1-22. doi: 10.3934/mcrf.2020024 |
[5] |
Pablo Neme, Jorge Oviedo. A note on the lattice structure for matching markets via linear programming. Journal of Dynamics & Games, 2020 doi: 10.3934/jdg.2021001 |
[6] |
Jie Li, Xiangdong Ye, Tao Yu. Mean equicontinuity, complexity and applications. Discrete & Continuous Dynamical Systems - A, 2021, 41 (1) : 359-393. doi: 10.3934/dcds.2020167 |
[7] |
Zhiyan Ding, Qin Li, Jianfeng Lu. Ensemble Kalman Inversion for nonlinear problems: Weights, consistency, and variance bounds. Foundations of Data Science, 2020 doi: 10.3934/fods.2020018 |
[8] |
Fabio Camilli, Giulia Cavagnari, Raul De Maio, Benedetto Piccoli. Superposition principle and schemes for measure differential equations. Kinetic & Related Models, 2021, 14 (1) : 89-113. doi: 10.3934/krm.2020050 |
[9] |
Manil T. Mohan. First order necessary conditions of optimality for the two dimensional tidal dynamics system. Mathematical Control & Related Fields, 2020 doi: 10.3934/mcrf.2020045 |
[10] |
Vaibhav Mehandiratta, Mani Mehra, Günter Leugering. Fractional optimal control problems on a star graph: Optimality system and numerical solution. Mathematical Control & Related Fields, 2021, 11 (1) : 189-209. doi: 10.3934/mcrf.2020033 |
[11] |
Giuseppina Guatteri, Federica Masiero. Stochastic maximum principle for problems with delay with dependence on the past through general measures. Mathematical Control & Related Fields, 2020 doi: 10.3934/mcrf.2020048 |
[12] |
Hui Lv, Xing'an Wang. Dissipative control for uncertain singular markovian jump systems via hybrid impulsive control. Numerical Algebra, Control & Optimization, 2021, 11 (1) : 127-142. doi: 10.3934/naco.2020020 |
[13] |
Hong Fu, Mingwu Liu, Bo Chen. Supplier's investment in manufacturer's quality improvement with equity holding. Journal of Industrial & Management Optimization, 2021, 17 (2) : 649-668. doi: 10.3934/jimo.2019127 |
[14] |
Skyler Simmons. Stability of broucke's isosceles orbit. Discrete & Continuous Dynamical Systems - A, 2021 doi: 10.3934/dcds.2021015 |
[15] |
Stefan Doboszczak, Manil T. Mohan, Sivaguru S. Sritharan. Pontryagin maximum principle for the optimal control of linearized compressible navier-stokes equations with state constraints. Evolution Equations & Control Theory, 2020 doi: 10.3934/eect.2020110 |
[16] |
François Ledrappier. Three problems solved by Sébastien Gouëzel. Journal of Modern Dynamics, 2020, 16: 373-387. doi: 10.3934/jmd.2020015 |
[17] |
Ugo Bessi. Another point of view on Kusuoka's measure. Discrete & Continuous Dynamical Systems - A, 2020 doi: 10.3934/dcds.2020404 |
[18] |
Illés Horváth, Kristóf Attila Horváth, Péter Kovács, Miklós Telek. Mean-field analysis of a scaling MAC radio protocol. Journal of Industrial & Management Optimization, 2021, 17 (1) : 279-297. doi: 10.3934/jimo.2019111 |
[19] |
Jian Zhang, Tony T. Lee, Tong Ye, Liang Huang. An approximate mean queue length formula for queueing systems with varying service rate. Journal of Industrial & Management Optimization, 2021, 17 (1) : 185-204. doi: 10.3934/jimo.2019106 |
[20] |
Laura Aquilanti, Simone Cacace, Fabio Camilli, Raul De Maio. A Mean Field Games model for finite mixtures of Bernoulli and categorical distributions. Journal of Dynamics & Games, 2020 doi: 10.3934/jdg.2020033 |
2019 Impact Factor: 1.366
Tools
Metrics
Other articles
by authors
[Back to Top]