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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), 215-236.
doi: 10.1111/j.1467-9965.2009.00362.x. |
[2] |
M. J. Brennan and Y. Xia, Dynamic asset allocation under inflation, Journal of Finance, 57 (2002), 1201-1238. |
[3] |
J. Cea, Lectures on Optimization - Theory and Algorithm, Tata Institute of Fundamental Research, Bombay, 1978. |
[4] |
S. N. Chen and W. T. Moore, Uncertain inflation and optimal portfolio selection: A simplified approach, The Financial Review, 20 (1985), 343-352.
doi: 10.1111/j.1540-6288.1985.tb00312.x. |
[5] |
C. H. Chiu and X. Y. Zhou, The premium of dynamic trading, Quantitative Finance, 11 (2011), 115-123.
doi: 10.1080/14697681003685589. |
[6] |
W. S. Fleming and H. M. Soner, Controlled Markov Processes and Viscosity Solutions, Springer-Verlag, New York, 1993. |
[7] |
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. |
[8] |
H. Markowitz, Portfolio selection, Journal of Finance, 7 (1952), 77-91. |
[9] |
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. |
[10] |
J. Z. Liu, L. H. Bai and K. F. C. Yiu, Optimal investment with a value-at-risk constraint, Journal of Industrial and Management Optimization, 8 (2012), 531-547.
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), 1889-1907.
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 regime-switching and risk constraint, Scandinavian Actuarial Journal, 2014 (2014), 583-601.
doi: 10.1080/03461238.2012.750621. |
[13] |
S. Manaster, Real and nominal efficient sets, Journal of Finance, 34 (1979), 93-102.
doi: 10.1111/j.1540-6261.1979.tb02073.x. |
[14] |
C. Munk, C. Sorensen and T. N. Vinther, Dynamic asset allocation under mean-reverting returns, stochastic interest rates and inflation uncertainty, International Review of Economics and Finance, 13 (2004), 141-166.
doi: 10.1016/j.iref.2003.08.001. |
[15] |
T. K. Siu, Long-term strategic asset allocation with inflation risk and regime switching, Quantitative Finance, 11 (2011), 1565-1580.
doi: 10.1080/14697680903055588. |
[16] |
B. H. Solnik, Inflation and optimal portfolio choice, Journal of Financial and Quantitative analysis, 13 (1978), 903-925.
doi: 10.2307/2330634. |
[17] |
A. Zhang, Stochastic Optimization in Finance and Life Insurance: Applications of the Martingale Method, Ph.D thesis, University of Kaiserslautern, 2008. |
[18] |
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. |
[19] |
K. F. C. Yiu, J. Z. Liu, T. K. Siu and W. C. Ching, Optimal portfolios with regime-switching and value-at-risk constraint, Automatica, 46 (2010), 979-989.
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), 215-236.
doi: 10.1111/j.1467-9965.2009.00362.x. |
[2] |
M. J. Brennan and Y. Xia, Dynamic asset allocation under inflation, Journal of Finance, 57 (2002), 1201-1238. |
[3] |
J. Cea, Lectures on Optimization - Theory and Algorithm, Tata Institute of Fundamental Research, Bombay, 1978. |
[4] |
S. N. Chen and W. T. Moore, Uncertain inflation and optimal portfolio selection: A simplified approach, The Financial Review, 20 (1985), 343-352.
doi: 10.1111/j.1540-6288.1985.tb00312.x. |
[5] |
C. H. Chiu and X. Y. Zhou, The premium of dynamic trading, Quantitative Finance, 11 (2011), 115-123.
doi: 10.1080/14697681003685589. |
[6] |
W. S. Fleming and H. M. Soner, Controlled Markov Processes and Viscosity Solutions, Springer-Verlag, New York, 1993. |
[7] |
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. |
[8] |
H. Markowitz, Portfolio selection, Journal of Finance, 7 (1952), 77-91. |
[9] |
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. |
[10] |
J. Z. Liu, L. H. Bai and K. F. C. Yiu, Optimal investment with a value-at-risk constraint, Journal of Industrial and Management Optimization, 8 (2012), 531-547.
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), 1889-1907.
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 regime-switching and risk constraint, Scandinavian Actuarial Journal, 2014 (2014), 583-601.
doi: 10.1080/03461238.2012.750621. |
[13] |
S. Manaster, Real and nominal efficient sets, Journal of Finance, 34 (1979), 93-102.
doi: 10.1111/j.1540-6261.1979.tb02073.x. |
[14] |
C. Munk, C. Sorensen and T. N. Vinther, Dynamic asset allocation under mean-reverting returns, stochastic interest rates and inflation uncertainty, International Review of Economics and Finance, 13 (2004), 141-166.
doi: 10.1016/j.iref.2003.08.001. |
[15] |
T. K. Siu, Long-term strategic asset allocation with inflation risk and regime switching, Quantitative Finance, 11 (2011), 1565-1580.
doi: 10.1080/14697680903055588. |
[16] |
B. H. Solnik, Inflation and optimal portfolio choice, Journal of Financial and Quantitative analysis, 13 (1978), 903-925.
doi: 10.2307/2330634. |
[17] |
A. Zhang, Stochastic Optimization in Finance and Life Insurance: Applications of the Martingale Method, Ph.D thesis, University of Kaiserslautern, 2008. |
[18] |
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. |
[19] |
K. F. C. Yiu, J. Z. Liu, T. K. Siu and W. C. Ching, Optimal portfolios with regime-switching and value-at-risk constraint, Automatica, 46 (2010), 979-989.
doi: 10.1016/j.automatica.2010.02.027. |
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