
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 multiperiod meanvariance 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 multiperiod risk adjusted values and Bellman's principle, Annals of Operations Research, 152 (2007), 522. doi: 10.1007/s1047900601326. 
[2] 
S. Basak and G. Chabakauri, Dynamic meanvariance asset allocation, Review of Financial Studies, 23 (2010), 29703016. 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), 13531381. 
[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), 124. doi: 10.1111/j.14679965.2011.00515.x. 
[6] 
K. Boda and J. A. Filar, Time consistent dynamic risk measures, Mathematical Methods of Operations Research, 63 (2006), 169186. doi: 10.1007/s0018600500451. 
[7] 
M. BrittenJones and A. Neuberger, Option prices, implied price processes, and stochastic volatility, Journal of Finance, 55 (2000), 839866. doi: 10.1111/00221082.00228. 
[8] 
U. Çakmak and S. Özekici, Portfolio optimization in stochastic markets, Mathematical Methods of Operations Research, 63 (2006), 151168. doi: 10.1007/s001860050020x. 
[9] 
E. Çanakoğlu and S. Özekici, Portfolio selection in stochastic markets with exponential utility functions, Annals of Operations Research, 166 (2009), 281297. doi: 10.1007/s1047900804062. 
[10] 
U. Çelikyurt and S. Özekici, Multiperiod portfolio optimization models in stochastic markets using the meanvariance approach, European Journal of Operational Research, 179 (2007), 186202. 
[11] 
Z. P. Chen, G. Li and J. E. Guo, Optimal investment policy in the time consistent meanvariance formulation, Insurance: Mathematics and Economics, 52 (2013), 145156. doi: 10.1016/j.insmatheco.2012.11.007. 
[12] 
Z. P. Chen, G. Li and Y. G. Zhao, Timeconsistent investment policies in Markovian markets: A case of meanvariance analysis, Journal of Economic Dynamic and Control, 40 (2014), 293316. doi: 10.1016/j.jedc.2014.01.011. 
[13] 
Z. P. Chen and J. Liu, Time consistent risk measure under twolevel 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, Twosided coherent risk measures and their application in realistic portfolio optimization, Journal of Banking and Finance, 32 (2008), 26672673. 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), 17771793. doi: 10.1016/j.jbankfin.2010.12.004. 
[16] 
P. Cheridito and M. Kupper, Composition of timeconsistent dynamic monetary risk measures in discrete time, Journal of Theoretical and Applied Finance, 14 (2011), 137162. doi: 10.1142/S0219024911006292. 
[17] 
X. Y. Cui, D. Li, S. Y. Wang and S. S. Zhu, Better than dynamic meanvariance: Time inconsistency and free cash flow stream, Mathematical Finance, 22 (2012), 346378. doi: 10.1111/j.14679965.2010.00461.x. 
[18] 
C. Czichowsky, Timeconsistent meanvariance portfolio selection in discrete and continuous time, Finance Stochastic, 17 (2013), 227271. doi: 10.1007/s0078001201899. 
[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), 196210. 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), 937969. doi: 10.2307/1913778. 
[21] 
H. Geman and S. Ohana, Timeconsistency in managing a commodity portfolio: A dynamic risk measure approach, Journal of Banking and Finance, 32 (2008), 19912005. 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), 12501269. doi: 10.1137/S0363012900377791. 
[23] 
D. Li and W. L. Ng, Optimal dynamic portfolio selection: Multiperiod meanvariance formulation, Mathematical Finance, 10 (2000), 387406. doi: 10.1111/14679965.00100. 
[24] 
X. Li, X. Y. Zhou and A. E. B. Lim, Dynamic meanvariance portfolio selection with noshorting constraints, SIAM Journal on Control and Optimization, 40 (2002), 15401555. 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), 541559. doi: 10.1007/s101070050628x. 
[26] 
F. Riedel, Dynamic coherent risk measures, Stochastic Processes and their Applications, 112 (2004), 185200. 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), 209230. doi: 10.1016/j.insmatheco.2006.04.003. 
[28] 
A. Ruszczyński, Riskaverse dynamic programming for Markov decision processes, Mathematical Programming, Series B, 125 (2010), 235261. doi: 10.1007/s1010701003933. 
[29] 
A. Shapiro, On a time consistency concept in risk averse multistage stochastic programming, Operations Research Letters, 37 (2009), 143147. doi: 10.1016/j.orl.2009.02.005. 
[30] 
M. C. Steinbach, Markowitz revisited: Meanvariance models in financial portfolio analysis, SIAM Review, 43 (2001), 3185. 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 timeconsistent strategy, European Journal of Operational Research, 209 (2011), 184201. doi: 10.1016/j.ejor.2010.09.038. 
[33] 
S. Z. Wei and Z. X. Ye, Multiperiod optimization portfolio with bankruptcy control in stochastic market, Applied Mathematics and Computation, 186 (2007), 414425. 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), 795815. doi: 10.3934/jimo.2014.10.795. 
[35] 
X. Y. Zhou and D. Li, Continuoustime meanvariance portfolio selection: A stochastic LQ framework, Applied Mathematics and Optimization, 42 (2000), 1933. doi: 10.1007/s002450010003. 
[36] 
S. S. Zhu, D. Li and S. Y. Wang, Risk control over bankruptcy in dynamic portfolio selection: A generalized meanvariance formulation, IEEE Transactions on Automatic Control, 49 (2004), 447457. doi: 10.1109/TAC.2004.824474. 
show all references
References:
[1] 
P. Artzner, F. Delbaen, J. M. Eber, D. Heath and H. Ku, Coherent multiperiod risk adjusted values and Bellman's principle, Annals of Operations Research, 152 (2007), 522. doi: 10.1007/s1047900601326. 
[2] 
S. Basak and G. Chabakauri, Dynamic meanvariance asset allocation, Review of Financial Studies, 23 (2010), 29703016. 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), 13531381. 
[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), 124. doi: 10.1111/j.14679965.2011.00515.x. 
[6] 
K. Boda and J. A. Filar, Time consistent dynamic risk measures, Mathematical Methods of Operations Research, 63 (2006), 169186. doi: 10.1007/s0018600500451. 
[7] 
M. BrittenJones and A. Neuberger, Option prices, implied price processes, and stochastic volatility, Journal of Finance, 55 (2000), 839866. doi: 10.1111/00221082.00228. 
[8] 
U. Çakmak and S. Özekici, Portfolio optimization in stochastic markets, Mathematical Methods of Operations Research, 63 (2006), 151168. doi: 10.1007/s001860050020x. 
[9] 
E. Çanakoğlu and S. Özekici, Portfolio selection in stochastic markets with exponential utility functions, Annals of Operations Research, 166 (2009), 281297. doi: 10.1007/s1047900804062. 
[10] 
U. Çelikyurt and S. Özekici, Multiperiod portfolio optimization models in stochastic markets using the meanvariance approach, European Journal of Operational Research, 179 (2007), 186202. 
[11] 
Z. P. Chen, G. Li and J. E. Guo, Optimal investment policy in the time consistent meanvariance formulation, Insurance: Mathematics and Economics, 52 (2013), 145156. doi: 10.1016/j.insmatheco.2012.11.007. 
[12] 
Z. P. Chen, G. Li and Y. G. Zhao, Timeconsistent investment policies in Markovian markets: A case of meanvariance analysis, Journal of Economic Dynamic and Control, 40 (2014), 293316. doi: 10.1016/j.jedc.2014.01.011. 
[13] 
Z. P. Chen and J. Liu, Time consistent risk measure under twolevel 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, Twosided coherent risk measures and their application in realistic portfolio optimization, Journal of Banking and Finance, 32 (2008), 26672673. 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), 17771793. doi: 10.1016/j.jbankfin.2010.12.004. 
[16] 
P. Cheridito and M. Kupper, Composition of timeconsistent dynamic monetary risk measures in discrete time, Journal of Theoretical and Applied Finance, 14 (2011), 137162. doi: 10.1142/S0219024911006292. 
[17] 
X. Y. Cui, D. Li, S. Y. Wang and S. S. Zhu, Better than dynamic meanvariance: Time inconsistency and free cash flow stream, Mathematical Finance, 22 (2012), 346378. doi: 10.1111/j.14679965.2010.00461.x. 
[18] 
C. Czichowsky, Timeconsistent meanvariance portfolio selection in discrete and continuous time, Finance Stochastic, 17 (2013), 227271. doi: 10.1007/s0078001201899. 
[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), 196210. 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), 937969. doi: 10.2307/1913778. 
[21] 
H. Geman and S. Ohana, Timeconsistency in managing a commodity portfolio: A dynamic risk measure approach, Journal of Banking and Finance, 32 (2008), 19912005. 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), 12501269. doi: 10.1137/S0363012900377791. 
[23] 
D. Li and W. L. Ng, Optimal dynamic portfolio selection: Multiperiod meanvariance formulation, Mathematical Finance, 10 (2000), 387406. doi: 10.1111/14679965.00100. 
[24] 
X. Li, X. Y. Zhou and A. E. B. Lim, Dynamic meanvariance portfolio selection with noshorting constraints, SIAM Journal on Control and Optimization, 40 (2002), 15401555. 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), 541559. doi: 10.1007/s101070050628x. 
[26] 
F. Riedel, Dynamic coherent risk measures, Stochastic Processes and their Applications, 112 (2004), 185200. 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), 209230. doi: 10.1016/j.insmatheco.2006.04.003. 
[28] 
A. Ruszczyński, Riskaverse dynamic programming for Markov decision processes, Mathematical Programming, Series B, 125 (2010), 235261. doi: 10.1007/s1010701003933. 
[29] 
A. Shapiro, On a time consistency concept in risk averse multistage stochastic programming, Operations Research Letters, 37 (2009), 143147. doi: 10.1016/j.orl.2009.02.005. 
[30] 
M. C. Steinbach, Markowitz revisited: Meanvariance models in financial portfolio analysis, SIAM Review, 43 (2001), 3185. 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 timeconsistent strategy, European Journal of Operational Research, 209 (2011), 184201. doi: 10.1016/j.ejor.2010.09.038. 
[33] 
S. Z. Wei and Z. X. Ye, Multiperiod optimization portfolio with bankruptcy control in stochastic market, Applied Mathematics and Computation, 186 (2007), 414425. 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), 795815. doi: 10.3934/jimo.2014.10.795. 
[35] 
X. Y. Zhou and D. Li, Continuoustime meanvariance portfolio selection: A stochastic LQ framework, Applied Mathematics and Optimization, 42 (2000), 1933. doi: 10.1007/s002450010003. 
[36] 
S. S. Zhu, D. Li and S. Y. Wang, Risk control over bankruptcy in dynamic portfolio selection: A generalized meanvariance formulation, IEEE Transactions on Automatic Control, 49 (2004), 447457. doi: 10.1109/TAC.2004.824474. 
[1] 
Nan Zhang, Ping Chen, Zhuo Jin, Shuanming Li. Markowitz's meanvariance optimization with investment and constrained reinsurance. Journal of Industrial and Management Optimization, 2017, 13 (1) : 375397. doi: 10.3934/jimo.2016022 
[2] 
Yu Jiang, Yiying Zhang, Peng Zhao. Optimal capital allocation for individual risk model using a MeanVariance Principle. Journal of Industrial and Management Optimization, 2022 doi: 10.3934/jimo.2022172 
[3] 
Liyuan Wang, Zhiping Chen, Peng Yang. Robust equilibrium controlmeasure policy for a DC pension plan with statedependent risk aversion under meanvariance criterion. Journal of Industrial and Management Optimization, 2021, 17 (3) : 12031233. doi: 10.3934/jimo.2020018 
[4] 
Ping Chen, Haixiang Yao. Continuoustime meanvariance portfolio selection with noshorting constraints and regimeswitching. Journal of Industrial and Management Optimization, 2020, 16 (2) : 531551. doi: 10.3934/jimo.2018166 
[5] 
HuaiNian Zhu, ChengKe Zhang, Zhuo Jin. Continuoustime meanvariance assetliability management with stochastic interest rates and inflation risks. Journal of Industrial and Management Optimization, 2020, 16 (2) : 813834. doi: 10.3934/jimo.2018180 
[6] 
Ishak Alia, Mohamed Sofiane Alia. Openloop equilibrium strategy for meanvariance Portfolio selection with investment constraints in a nonMarkovian regimeswitching jumpdiffusion model. Journal of Industrial and Management Optimization, 2022 doi: 10.3934/jimo.2022048 
[7] 
Lihua Bian, Zhongfei Li, Haixiang Yao. Timeconsistent strategy for a multiperiod meanvariance assetliability management problem with stochastic interest rate. Journal of Industrial and Management Optimization, 2021, 17 (3) : 13831410. doi: 10.3934/jimo.2020026 
[8] 
Yingxu Tian, Junyi Guo, Zhongyang Sun. Optimal meanvariance reinsurance in a financial market with stochastic rate of return. Journal of Industrial and Management Optimization, 2021, 17 (4) : 18871912. doi: 10.3934/jimo.2020051 
[9] 
Yan Zeng, Zhongfei Li, Jingjun Liu. Optimal strategies of benchmark and meanvariance portfolio selection problems for insurers. Journal of Industrial and Management Optimization, 2010, 6 (3) : 483496. doi: 10.3934/jimo.2010.6.483 
[10] 
Jingzhen Liu, KaFai Cedric Yiu, Xun Li, Tak Kuen Siu, Kok Lay Teo. Meanvariance portfolio selection with random investment horizon. Journal of Industrial and Management Optimization, 2022 doi: 10.3934/jimo.2022147 
[11] 
Jiannan Zhang, Ping Chen, Zhuo Jin, Shuanming Li. Openloop equilibrium strategy for meanvariance portfolio selection: A logreturn model. Journal of Industrial and Management Optimization, 2021, 17 (2) : 765777. doi: 10.3934/jimo.2019133 
[12] 
Shuang Li, Chuong Luong, Francisca Angkola, Yonghong Wu. Optimal asset portfolio with stochastic volatility under the meanvariance utility with statedependent risk aversion. Journal of Industrial and Management Optimization, 2016, 12 (4) : 15211533. doi: 10.3934/jimo.2016.12.1521 
[13] 
Haixiang Yao, Zhongfei Li, Yongzeng Lai. Dynamic meanvariance asset allocation with stochastic interest rate and inflation rate. Journal of Industrial and Management Optimization, 2016, 12 (1) : 187209. doi: 10.3934/jimo.2016.12.187 
[14] 
Zhen Wang, Sanyang Liu. Multiperiod meanvariance portfolio selection with fixed and proportional transaction costs. Journal of Industrial and Management Optimization, 2013, 9 (3) : 643657. doi: 10.3934/jimo.2013.9.643 
[15] 
Ning Zhang. A symmetric GaussSeidel based method for a class of multiperiod meanvariance portfolio selection problems. Journal of Industrial and Management Optimization, 2020, 16 (2) : 9911008. doi: 10.3934/jimo.2018189 
[16] 
Qian Zhao, Yang Shen, Jiaqin Wei. Meanvariance investment and contribution decisions for defined benefit pension plans in a stochastic framework. Journal of Industrial and Management Optimization, 2021, 17 (3) : 11471171. doi: 10.3934/jimo.2020015 
[17] 
Hao Chang, Jiaao Li, Hui Zhao. Robust optimal strategies of DC pension plans with stochastic volatility and stochastic income under meanvariance criteria. Journal of Industrial and Management Optimization, 2022, 18 (2) : 13931423. doi: 10.3934/jimo.2021025 
[18] 
Liming Zhang, Rongming Wang, Jiaqin Wei. Openloop equilibrium meanvariance reinsurance, new business and investment strategies with constraints. Journal of Industrial and Management Optimization, 2022, 18 (6) : 38973927. doi: 10.3934/jimo.2021140 
[19] 
Xianping Wu, Xun Li, Zhongfei Li. A meanfield formulation for multiperiod assetliability meanvariance portfolio selection with probability constraints. Journal of Industrial and Management Optimization, 2018, 14 (1) : 249265. doi: 10.3934/jimo.2017045 
[20] 
Yumo Zhang. Meanvariance assetliability management under CIR interest rate and the family of 4/2 stochastic volatility models with derivative trading. Journal of Industrial and Management Optimization, 2022 doi: 10.3934/jimo.2022121 
2021 Impact Factor: 1.411
Tools
Metrics
Other articles
by authors
[Back to Top]