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Robust output stabilization for a class of nonlinear uncertain stochastic systems under multiplicative and additive noises: The attractive ellipsoid method
Dynamic mean-variance asset allocation with stochastic interest rate and inflation rate
1. | School of Finance, Guangdong University of Foreign Studies, Guangzhou 510006, China |
2. | Lingnan (University) College/Sun Yat-sen Business School, Sun Yat-sen University, Guangzhou 510275 |
3. | Department of Mathematics, Wilfrid Laurier University, Waterloo, Ontario, N2L 3C5, Canada |
References:
[1] |
I. Bajeux-Besnainou and R. Portait, Dynamic asset allocation in a mean-variance framework, Management Science, 44 (1998), S79-S95. |
[2] |
T. R. Bielecki, H. Q. Jin, S. R. Pliska and X. Y. Zhou, Continuous-time mean-variance portfolio selection with bankruptcy prohibition, Mathematical Finance, 15 (2005), 213-244.
doi: 10.1111/j.0960-1627.2005.00218.x. |
[3] |
M. J. Brennan and Y. Xia, Dynamic asset allocation under inflation, Journal of Finance, 57 (2002), 1201-1238.
doi: 10.1111/1540-6261.00459. |
[4] |
T. Chellathurai and T. Draviam, Dynamic portfolio selection with fixed and/or proportional transaction costs using non-singular stochastic optimal control theory, Journal of Economic Dynamics and Control, 31 (2007), 2168-2195.
doi: 10.1016/j.jedc.2006.06.006. |
[5] |
P. Chen, H. L. Yang and G. Yin, Markowitz's mean-variance asset-liability management with regime switching: A continuous-time model, Insurance: Mathematics and Economics, 43 (2008), 456-465.
doi: 10.1016/j.insmatheco.2008.09.001. |
[6] |
Y. Y. Chou, N. W. Han and M. W. Hung, Optimal portfolio-consumption choice under stochastic inflation with nominal and indexed bonds, Applied Stochastic Models in Business and Industry, 27 (2011), 691-706.
doi: 10.1002/asmb.886. |
[7] |
O. L. V. Costa and A. D. Oliveira, Optimal mean-variance control for discrete-time linear systems with Markovian jumps and multiplicative noises, Automatica, 48 (2012), 304-315.
doi: 10.1016/j.automatica.2011.11.009. |
[8] |
R. Ferland and F. Watier, Mean-variance efficiency with extended CIR interest rates, Applied Stochastic Models in Business and Industry, 26 (2010), 71-84.
doi: 10.1002/asmb.767. |
[9] |
W. H. Fleming and H. M. Soner, Controlled Markov Processes and Viscosity Solutions, 2ed. Springer, New York, 2006. |
[10] |
C. P. Fu, A. Lari-lavassani and X. Li, Dynamic mean-variance portfolio selection with borrowing constraint, European Journal of Operational Research, 200 (2010), 313-319.
doi: 10.1016/j.ejor.2009.01.005. |
[11] |
J. W. Gao, Stochastic optimal control of DC pension funds, Insurance: Mathematics and Economics, 42 (2008), 1159-1164.
doi: 10.1016/j.insmatheco.2008.03.004. |
[12] |
D. Hainaut, Dynamic asset allocation under VaR constraint with stochastic interest rates, Annals Of Operations Research, 172 (2009), 97-117.
doi: 10.1007/s10479-008-0509-9. |
[13] |
N. W. Han and M. W. Hung, Optimal asset allocation for DC pension plans under inflation, Insurance: Mathematics and Economics, 51 (2012), 172-181.
doi: 10.1016/j.insmatheco.2012.03.003. |
[14] |
R. Josa-Fombellida and J. P. Rincón-Zapatero, Optimal asset allocation for aggregated defined benefit pension funds with stochastic interest rates, European Journal of Operational Research, 201 (2010), 211-221. |
[15] |
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. |
[16] |
P. Lakner and L. M. Nygren, Portfolio optimization with downside constraints, Mathematical Finance, 16 (2006), 283-299.
doi: 10.1111/j.1467-9965.2006.00272.x. |
[17] |
M. Leippold, F. Trojani and P. Vanini, Multiperiod mean-variance efficient portfolios with endogenous liabilities, Quantitative Finance, 11 (2011), 1535-1546.
doi: 10.1080/14697680902950813. |
[18] |
D. Li and W. L. Ng, Optimal dynamic portfolio selection: Multiperiod mean-variance formulation, Mathematical Finance, 10 (2000), 387-406. |
[19] |
X. Li and X. Y. Zhou, Continuous-time mean-variance efficiency: The 80 The Annals of Applied Probability, 16 (2006), 1751-1763.
doi: 10.1214/105051606000000349. |
[20] |
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. |
[21] |
A. E. B. Lim and X. Y. Zhou, Mean-variance portfolio selection with random parameters in a complete market, Mathematics of Operations Research, 27 (2002), 101-120. |
[22] |
D. G. Luenberger, Optimization by Vector Space Methods, Wiley, New York, 1969. |
[23] |
H. Markowitz, Portfolio selection, Journal of Finance, 7 (1952), 77-91. |
[24] |
R. C. Merton, Lifetime portfolio selection under uncertainty: The continuous-time model, Review of Economic and Statistics, 51 (1969), 247-256. |
[25] |
C. Munk and C. Sørensen, Optimal consumption and investment strategies with stochastic interest rates, Journal of Banking & Finance, 28 (2004), 1987-2013.
doi: 10.1016/j.jbankfin.2003.07.002. |
[26] |
C. Munk and C. Sørensen, Dynamic asset allocation with stochastic income and interest rates, Journal of Financial Economics, 96 (2010), 433-462.
doi: 10.1016/j.jfineco.2010.01.004. |
[27] |
C. Munk and C. Sørensen and T. N. Vinther, Dynamic asset allocation under mean-reverting returns, stochastic interest rates, and inflation uncertainty: Are popular recommendations consistent with rational behavior?, International Review of Economics and Finance, 13 (2004), 141-166. |
[28] |
P. A. Samuelson, Lifetime portfolio selection by dynamic stochastic programming, Review of Economics and Statistics, 51 (1969), 239-246.
doi: 10.2307/1926559. |
[29] |
Z. Wang and S. Y. Liu, Multi-period mean-variance portfolio selection with fixed and proportional transaction costs, Journal of Industrial and Management Optimization, 9 (2013), 643-657.
doi: 10.3934/jimo.2013.9.643. |
[30] |
H. L. Wu, Mean-variance portfolio selection with a stochastic cash flow in a markov-switching jump-diffusion market, Journal of Optimization Theory and Applications, 158 (2013), 918-934.
doi: 10.1007/s10957-013-0292-x. |
[31] |
H. X. Yao, Y. Z. Lai and Y. Li, Continuous-time mean-variance asset-liability management with endogenous liabilities, Insurance: Mathematics and Economics, 52 (2013), 6-17.
doi: 10.1016/j.insmatheco.2012.10.001. |
[32] |
H. X. Yao, Y. Z. Lai and Z. F. Hao, Uncertain exit time multi-period mean-variance portfolio selection with endogenous liabilities and Markov jumps, Automatica, 49 (2013), 3258-3269.
doi: 10.1016/j.automatica.2013.08.023. |
[33] |
L. Yi, Z. F. Li and D. Li, Mutli-period portfolio selection for asset-liability management with uncertain investment horizon, Journal of Industrial and Management Optimization, 4 (2008), 535-552.
doi: 10.3934/jimo.2008.4.535. |
[34] |
H. L. Yuan and Y. J. Hu, Optimal consumption and portfolio policies with the consumption habit constraints and the terminal wealth downside constraints, Insurance: Mathematics and Economics, 45 (2009), 405-409.
doi: 10.1016/j.insmatheco.2009.08.012. |
[35] |
A. Zhang and C. O. Ewald, Optimal investment for a pension fund under inflation risk, Mathematical Methods of Operations Research, 71 (2010), 353-369.
doi: 10.1007/s00186-009-0294-5. |
[36] |
Y. Zeng, Z. F. Li and J. J. Liu, Optimal Strategies Of Benchmark And Mean-Variance Portfolio Selection Problems For Insurers, Journal of Industrial and Management Optimization, 6 (2010), 483-496.
doi: 10.3934/jimo.2010.6.483. |
[37] |
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. |
show all references
References:
[1] |
I. Bajeux-Besnainou and R. Portait, Dynamic asset allocation in a mean-variance framework, Management Science, 44 (1998), S79-S95. |
[2] |
T. R. Bielecki, H. Q. Jin, S. R. Pliska and X. Y. Zhou, Continuous-time mean-variance portfolio selection with bankruptcy prohibition, Mathematical Finance, 15 (2005), 213-244.
doi: 10.1111/j.0960-1627.2005.00218.x. |
[3] |
M. J. Brennan and Y. Xia, Dynamic asset allocation under inflation, Journal of Finance, 57 (2002), 1201-1238.
doi: 10.1111/1540-6261.00459. |
[4] |
T. Chellathurai and T. Draviam, Dynamic portfolio selection with fixed and/or proportional transaction costs using non-singular stochastic optimal control theory, Journal of Economic Dynamics and Control, 31 (2007), 2168-2195.
doi: 10.1016/j.jedc.2006.06.006. |
[5] |
P. Chen, H. L. Yang and G. Yin, Markowitz's mean-variance asset-liability management with regime switching: A continuous-time model, Insurance: Mathematics and Economics, 43 (2008), 456-465.
doi: 10.1016/j.insmatheco.2008.09.001. |
[6] |
Y. Y. Chou, N. W. Han and M. W. Hung, Optimal portfolio-consumption choice under stochastic inflation with nominal and indexed bonds, Applied Stochastic Models in Business and Industry, 27 (2011), 691-706.
doi: 10.1002/asmb.886. |
[7] |
O. L. V. Costa and A. D. Oliveira, Optimal mean-variance control for discrete-time linear systems with Markovian jumps and multiplicative noises, Automatica, 48 (2012), 304-315.
doi: 10.1016/j.automatica.2011.11.009. |
[8] |
R. Ferland and F. Watier, Mean-variance efficiency with extended CIR interest rates, Applied Stochastic Models in Business and Industry, 26 (2010), 71-84.
doi: 10.1002/asmb.767. |
[9] |
W. H. Fleming and H. M. Soner, Controlled Markov Processes and Viscosity Solutions, 2ed. Springer, New York, 2006. |
[10] |
C. P. Fu, A. Lari-lavassani and X. Li, Dynamic mean-variance portfolio selection with borrowing constraint, European Journal of Operational Research, 200 (2010), 313-319.
doi: 10.1016/j.ejor.2009.01.005. |
[11] |
J. W. Gao, Stochastic optimal control of DC pension funds, Insurance: Mathematics and Economics, 42 (2008), 1159-1164.
doi: 10.1016/j.insmatheco.2008.03.004. |
[12] |
D. Hainaut, Dynamic asset allocation under VaR constraint with stochastic interest rates, Annals Of Operations Research, 172 (2009), 97-117.
doi: 10.1007/s10479-008-0509-9. |
[13] |
N. W. Han and M. W. Hung, Optimal asset allocation for DC pension plans under inflation, Insurance: Mathematics and Economics, 51 (2012), 172-181.
doi: 10.1016/j.insmatheco.2012.03.003. |
[14] |
R. Josa-Fombellida and J. P. Rincón-Zapatero, Optimal asset allocation for aggregated defined benefit pension funds with stochastic interest rates, European Journal of Operational Research, 201 (2010), 211-221. |
[15] |
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. |
[16] |
P. Lakner and L. M. Nygren, Portfolio optimization with downside constraints, Mathematical Finance, 16 (2006), 283-299.
doi: 10.1111/j.1467-9965.2006.00272.x. |
[17] |
M. Leippold, F. Trojani and P. Vanini, Multiperiod mean-variance efficient portfolios with endogenous liabilities, Quantitative Finance, 11 (2011), 1535-1546.
doi: 10.1080/14697680902950813. |
[18] |
D. Li and W. L. Ng, Optimal dynamic portfolio selection: Multiperiod mean-variance formulation, Mathematical Finance, 10 (2000), 387-406. |
[19] |
X. Li and X. Y. Zhou, Continuous-time mean-variance efficiency: The 80 The Annals of Applied Probability, 16 (2006), 1751-1763.
doi: 10.1214/105051606000000349. |
[20] |
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. |
[21] |
A. E. B. Lim and X. Y. Zhou, Mean-variance portfolio selection with random parameters in a complete market, Mathematics of Operations Research, 27 (2002), 101-120. |
[22] |
D. G. Luenberger, Optimization by Vector Space Methods, Wiley, New York, 1969. |
[23] |
H. Markowitz, Portfolio selection, Journal of Finance, 7 (1952), 77-91. |
[24] |
R. C. Merton, Lifetime portfolio selection under uncertainty: The continuous-time model, Review of Economic and Statistics, 51 (1969), 247-256. |
[25] |
C. Munk and C. Sørensen, Optimal consumption and investment strategies with stochastic interest rates, Journal of Banking & Finance, 28 (2004), 1987-2013.
doi: 10.1016/j.jbankfin.2003.07.002. |
[26] |
C. Munk and C. Sørensen, Dynamic asset allocation with stochastic income and interest rates, Journal of Financial Economics, 96 (2010), 433-462.
doi: 10.1016/j.jfineco.2010.01.004. |
[27] |
C. Munk and C. Sørensen and T. N. Vinther, Dynamic asset allocation under mean-reverting returns, stochastic interest rates, and inflation uncertainty: Are popular recommendations consistent with rational behavior?, International Review of Economics and Finance, 13 (2004), 141-166. |
[28] |
P. A. Samuelson, Lifetime portfolio selection by dynamic stochastic programming, Review of Economics and Statistics, 51 (1969), 239-246.
doi: 10.2307/1926559. |
[29] |
Z. Wang and S. Y. Liu, Multi-period mean-variance portfolio selection with fixed and proportional transaction costs, Journal of Industrial and Management Optimization, 9 (2013), 643-657.
doi: 10.3934/jimo.2013.9.643. |
[30] |
H. L. Wu, Mean-variance portfolio selection with a stochastic cash flow in a markov-switching jump-diffusion market, Journal of Optimization Theory and Applications, 158 (2013), 918-934.
doi: 10.1007/s10957-013-0292-x. |
[31] |
H. X. Yao, Y. Z. Lai and Y. Li, Continuous-time mean-variance asset-liability management with endogenous liabilities, Insurance: Mathematics and Economics, 52 (2013), 6-17.
doi: 10.1016/j.insmatheco.2012.10.001. |
[32] |
H. X. Yao, Y. Z. Lai and Z. F. Hao, Uncertain exit time multi-period mean-variance portfolio selection with endogenous liabilities and Markov jumps, Automatica, 49 (2013), 3258-3269.
doi: 10.1016/j.automatica.2013.08.023. |
[33] |
L. Yi, Z. F. Li and D. Li, Mutli-period portfolio selection for asset-liability management with uncertain investment horizon, Journal of Industrial and Management Optimization, 4 (2008), 535-552.
doi: 10.3934/jimo.2008.4.535. |
[34] |
H. L. Yuan and Y. J. Hu, Optimal consumption and portfolio policies with the consumption habit constraints and the terminal wealth downside constraints, Insurance: Mathematics and Economics, 45 (2009), 405-409.
doi: 10.1016/j.insmatheco.2009.08.012. |
[35] |
A. Zhang and C. O. Ewald, Optimal investment for a pension fund under inflation risk, Mathematical Methods of Operations Research, 71 (2010), 353-369.
doi: 10.1007/s00186-009-0294-5. |
[36] |
Y. Zeng, Z. F. Li and J. J. Liu, Optimal Strategies Of Benchmark And Mean-Variance Portfolio Selection Problems For Insurers, Journal of Industrial and Management Optimization, 6 (2010), 483-496.
doi: 10.3934/jimo.2010.6.483. |
[37] |
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. |
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