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The optimal mean variance problem with inflation
1.  School of Insurance, Central University of Finance and Economics, Beijing 10086, China 
2.  Department of Applied Mathematics, The Hong Kong Polytechnic University, Hunghom, Kowloon, Hong Kong, China 
3.  Department of Systems Engineering and Engineering Management, City University of Hong Kong, Kowloon Tong, Hong Kong, China 
References:
[1] 
A. Bensoussan, J. Keppo and S. P. Sethi, Optimal consumption and portfolio decisions with partially observed real prices,, Mathematical Finance, 19 (2009), 215. doi: 10.1111/j.14679965.2009.00362.x. 
[2] 
M. J. Brennan and Y. Xia, Dynamic asset allocation under inflation,, Journal of Finance, 57 (2002), 1201. 
[3] 
J. Cea, Lectures on Optimization  Theory and Algorithm,, Tata Institute of Fundamental Research, (1978). 
[4] 
S. N. Chen and W. T. Moore, Uncertain inflation and optimal portfolio selection: A simplified approach,, The Financial Review, 20 (1985), 343. doi: 10.1111/j.15406288.1985.tb00312.x. 
[5] 
C. H. Chiu and X. Y. Zhou, The premium of dynamic trading,, Quantitative Finance, 11 (2011), 115. doi: 10.1080/14697681003685589. 
[6] 
W. S. Fleming and H. M. Soner, Controlled Markov Processes and Viscosity Solutions,, SpringerVerlag, (1993). 
[7] 
D. Li and W. L. Ng, Optimal dynamic portfolio selection: Multiperiod meanvariance formulation,, Mathematical Finance, 10 (2000), 387. doi: 10.1111/14679965.00100. 
[8] 
H. Markowitz, Portfolio selection,, Journal of Finance, 7 (1952), 77. 
[9] 
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), 1540. doi: 10.1137/S0363012900378504. 
[10] 
J. Z. Liu, L. H. Bai and K. F. C. Yiu, Optimal investment with a valueatrisk constraint,, Journal of Industrial and Management Optimization, 8 (2012), 531. doi: 10.3934/jimo.2012.8.531. 
[11] 
J. Z. Liu and K. F. C. Yiu, Optimal stochastic differential games with VaR constraint,, Discrete & Continuous Dynamical Systems  Series B, 18 (2013), 1889. doi: 10.3934/dcdsb.2013.18.1889. 
[12] 
J. Z. Liu, K. F. C. Yiu and T. K. Siu, Optimal investment of an insurer with regimeswitching and risk constraint,, Scandinavian Actuarial Journal, 2014 (2014), 583. doi: 10.1080/03461238.2012.750621. 
[13] 
S. Manaster, Real and nominal efficient sets,, Journal of Finance, 34 (1979), 93. doi: 10.1111/j.15406261.1979.tb02073.x. 
[14] 
C. Munk, C. Sorensen and T. N. Vinther, Dynamic asset allocation under meanreverting returns, stochastic interest rates and inflation uncertainty,, International Review of Economics and Finance, 13 (2004), 141. doi: 10.1016/j.iref.2003.08.001. 
[15] 
T. K. Siu, Longterm strategic asset allocation with inflation risk and regime switching,, Quantitative Finance, 11 (2011), 1565. doi: 10.1080/14697680903055588. 
[16] 
B. H. Solnik, Inflation and optimal portfolio choice,, Journal of Financial and Quantitative analysis, 13 (1978), 903. doi: 10.2307/2330634. 
[17] 
A. Zhang, Stochastic Optimization in Finance and Life Insurance: Applications of the Martingale Method,, Ph.D thesis, (2008). 
[18] 
X. Y. Zhou and D. Li, Continuoustime meanvariance portfolio selection: A stochastic LQ framework,, Applied Mathematics and Optimization, 42 (2000), 19. doi: 10.1007/s002450010003. 
[19] 
K. F. C. Yiu, J. Z. Liu, T. K. Siu and W. C. Ching, Optimal portfolios with regimeswitching and valueatrisk constraint,, Automatica, 46 (2010), 979. doi: 10.1016/j.automatica.2010.02.027. 
show all references
References:
[1] 
A. Bensoussan, J. Keppo and S. P. Sethi, Optimal consumption and portfolio decisions with partially observed real prices,, Mathematical Finance, 19 (2009), 215. doi: 10.1111/j.14679965.2009.00362.x. 
[2] 
M. J. Brennan and Y. Xia, Dynamic asset allocation under inflation,, Journal of Finance, 57 (2002), 1201. 
[3] 
J. Cea, Lectures on Optimization  Theory and Algorithm,, Tata Institute of Fundamental Research, (1978). 
[4] 
S. N. Chen and W. T. Moore, Uncertain inflation and optimal portfolio selection: A simplified approach,, The Financial Review, 20 (1985), 343. doi: 10.1111/j.15406288.1985.tb00312.x. 
[5] 
C. H. Chiu and X. Y. Zhou, The premium of dynamic trading,, Quantitative Finance, 11 (2011), 115. doi: 10.1080/14697681003685589. 
[6] 
W. S. Fleming and H. M. Soner, Controlled Markov Processes and Viscosity Solutions,, SpringerVerlag, (1993). 
[7] 
D. Li and W. L. Ng, Optimal dynamic portfolio selection: Multiperiod meanvariance formulation,, Mathematical Finance, 10 (2000), 387. doi: 10.1111/14679965.00100. 
[8] 
H. Markowitz, Portfolio selection,, Journal of Finance, 7 (1952), 77. 
[9] 
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), 1540. doi: 10.1137/S0363012900378504. 
[10] 
J. Z. Liu, L. H. Bai and K. F. C. Yiu, Optimal investment with a valueatrisk constraint,, Journal of Industrial and Management Optimization, 8 (2012), 531. doi: 10.3934/jimo.2012.8.531. 
[11] 
J. Z. Liu and K. F. C. Yiu, Optimal stochastic differential games with VaR constraint,, Discrete & Continuous Dynamical Systems  Series B, 18 (2013), 1889. doi: 10.3934/dcdsb.2013.18.1889. 
[12] 
J. Z. Liu, K. F. C. Yiu and T. K. Siu, Optimal investment of an insurer with regimeswitching and risk constraint,, Scandinavian Actuarial Journal, 2014 (2014), 583. doi: 10.1080/03461238.2012.750621. 
[13] 
S. Manaster, Real and nominal efficient sets,, Journal of Finance, 34 (1979), 93. doi: 10.1111/j.15406261.1979.tb02073.x. 
[14] 
C. Munk, C. Sorensen and T. N. Vinther, Dynamic asset allocation under meanreverting returns, stochastic interest rates and inflation uncertainty,, International Review of Economics and Finance, 13 (2004), 141. doi: 10.1016/j.iref.2003.08.001. 
[15] 
T. K. Siu, Longterm strategic asset allocation with inflation risk and regime switching,, Quantitative Finance, 11 (2011), 1565. doi: 10.1080/14697680903055588. 
[16] 
B. H. Solnik, Inflation and optimal portfolio choice,, Journal of Financial and Quantitative analysis, 13 (1978), 903. doi: 10.2307/2330634. 
[17] 
A. Zhang, Stochastic Optimization in Finance and Life Insurance: Applications of the Martingale Method,, Ph.D thesis, (2008). 
[18] 
X. Y. Zhou and D. Li, Continuoustime meanvariance portfolio selection: A stochastic LQ framework,, Applied Mathematics and Optimization, 42 (2000), 19. doi: 10.1007/s002450010003. 
[19] 
K. F. C. Yiu, J. Z. Liu, T. K. Siu and W. C. Ching, Optimal portfolios with regimeswitching and valueatrisk constraint,, Automatica, 46 (2010), 979. doi: 10.1016/j.automatica.2010.02.027. 
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