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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 meanvariance 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 Yatsen Business School, Sun Yatsen University, Guangzhou 510275 
3.  Department of Mathematics, Wilfrid Laurier University, Waterloo, Ontario, N2L 3C5, Canada 
References:
[1] 
I. BajeuxBesnainou and R. Portait, Dynamic asset allocation in a meanvariance framework, Management Science, 44 (1998), S79S95. 
[2] 
T. R. Bielecki, H. Q. Jin, S. R. Pliska and X. Y. Zhou, Continuoustime meanvariance portfolio selection with bankruptcy prohibition, Mathematical Finance, 15 (2005), 213244. doi: 10.1111/j.09601627.2005.00218.x. 
[3] 
M. J. Brennan and Y. Xia, Dynamic asset allocation under inflation, Journal of Finance, 57 (2002), 12011238. doi: 10.1111/15406261.00459. 
[4] 
T. Chellathurai and T. Draviam, Dynamic portfolio selection with fixed and/or proportional transaction costs using nonsingular stochastic optimal control theory, Journal of Economic Dynamics and Control, 31 (2007), 21682195. doi: 10.1016/j.jedc.2006.06.006. 
[5] 
P. Chen, H. L. Yang and G. Yin, Markowitz's meanvariance assetliability management with regime switching: A continuoustime model, Insurance: Mathematics and Economics, 43 (2008), 456465. doi: 10.1016/j.insmatheco.2008.09.001. 
[6] 
Y. Y. Chou, N. W. Han and M. W. Hung, Optimal portfolioconsumption choice under stochastic inflation with nominal and indexed bonds, Applied Stochastic Models in Business and Industry, 27 (2011), 691706. doi: 10.1002/asmb.886. 
[7] 
O. L. V. Costa and A. D. Oliveira, Optimal meanvariance control for discretetime linear systems with Markovian jumps and multiplicative noises, Automatica, 48 (2012), 304315. doi: 10.1016/j.automatica.2011.11.009. 
[8] 
R. Ferland and F. Watier, Meanvariance efficiency with extended CIR interest rates, Applied Stochastic Models in Business and Industry, 26 (2010), 7184. 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. Larilavassani and X. Li, Dynamic meanvariance portfolio selection with borrowing constraint, European Journal of Operational Research, 200 (2010), 313319. 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), 11591164. 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), 97117. doi: 10.1007/s1047900805099. 
[13] 
N. W. Han and M. W. Hung, Optimal asset allocation for DC pension plans under inflation, Insurance: Mathematics and Economics, 51 (2012), 172181. doi: 10.1016/j.insmatheco.2012.03.003. 
[14] 
R. JosaFombellida and J. P. RincónZapatero, Optimal asset allocation for aggregated defined benefit pension funds with stochastic interest rates, European Journal of Operational Research, 201 (2010), 211221. 
[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), 12501269. doi: 10.1137/S0363012900377791. 
[16] 
P. Lakner and L. M. Nygren, Portfolio optimization with downside constraints, Mathematical Finance, 16 (2006), 283299. doi: 10.1111/j.14679965.2006.00272.x. 
[17] 
M. Leippold, F. Trojani and P. Vanini, Multiperiod meanvariance efficient portfolios with endogenous liabilities, Quantitative Finance, 11 (2011), 15351546. doi: 10.1080/14697680902950813. 
[18] 
D. Li and W. L. Ng, Optimal dynamic portfolio selection: Multiperiod meanvariance formulation, Mathematical Finance, 10 (2000), 387406. 
[19] 
X. Li and X. Y. Zhou, Continuoustime meanvariance efficiency: The 80 The Annals of Applied Probability, 16 (2006), 17511763. doi: 10.1214/105051606000000349. 
[20] 
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. 
[21] 
A. E. B. Lim and X. Y. Zhou, Meanvariance portfolio selection with random parameters in a complete market, Mathematics of Operations Research, 27 (2002), 101120. 
[22] 
D. G. Luenberger, Optimization by Vector Space Methods, Wiley, New York, 1969. 
[23] 
H. Markowitz, Portfolio selection, Journal of Finance, 7 (1952), 7791. 
[24] 
R. C. Merton, Lifetime portfolio selection under uncertainty: The continuoustime model, Review of Economic and Statistics, 51 (1969), 247256. 
[25] 
C. Munk and C. Sørensen, Optimal consumption and investment strategies with stochastic interest rates, Journal of Banking & Finance, 28 (2004), 19872013. 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), 433462. doi: 10.1016/j.jfineco.2010.01.004. 
[27] 
C. Munk and C. Sørensen and T. N. Vinther, Dynamic asset allocation under meanreverting returns, stochastic interest rates, and inflation uncertainty: Are popular recommendations consistent with rational behavior?, International Review of Economics and Finance, 13 (2004), 141166. 
[28] 
P. A. Samuelson, Lifetime portfolio selection by dynamic stochastic programming, Review of Economics and Statistics, 51 (1969), 239246. doi: 10.2307/1926559. 
[29] 
Z. Wang and S. Y. Liu, Multiperiod meanvariance portfolio selection with fixed and proportional transaction costs, Journal of Industrial and Management Optimization, 9 (2013), 643657. doi: 10.3934/jimo.2013.9.643. 
[30] 
H. L. Wu, Meanvariance portfolio selection with a stochastic cash flow in a markovswitching jumpdiffusion market, Journal of Optimization Theory and Applications, 158 (2013), 918934. doi: 10.1007/s109570130292x. 
[31] 
H. X. Yao, Y. Z. Lai and Y. Li, Continuoustime meanvariance assetliability management with endogenous liabilities, Insurance: Mathematics and Economics, 52 (2013), 617. doi: 10.1016/j.insmatheco.2012.10.001. 
[32] 
H. X. Yao, Y. Z. Lai and Z. F. Hao, Uncertain exit time multiperiod meanvariance portfolio selection with endogenous liabilities and Markov jumps, Automatica, 49 (2013), 32583269. doi: 10.1016/j.automatica.2013.08.023. 
[33] 
L. Yi, Z. F. Li and D. Li, Mutliperiod portfolio selection for assetliability management with uncertain investment horizon, Journal of Industrial and Management Optimization, 4 (2008), 535552. 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), 405409. 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), 353369. doi: 10.1007/s0018600902945. 
[36] 
Y. Zeng, Z. F. Li and J. J. Liu, Optimal Strategies Of Benchmark And MeanVariance Portfolio Selection Problems For Insurers, Journal of Industrial and Management Optimization, 6 (2010), 483496. doi: 10.3934/jimo.2010.6.483. 
[37] 
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. 
show all references
References:
[1] 
I. BajeuxBesnainou and R. Portait, Dynamic asset allocation in a meanvariance framework, Management Science, 44 (1998), S79S95. 
[2] 
T. R. Bielecki, H. Q. Jin, S. R. Pliska and X. Y. Zhou, Continuoustime meanvariance portfolio selection with bankruptcy prohibition, Mathematical Finance, 15 (2005), 213244. doi: 10.1111/j.09601627.2005.00218.x. 
[3] 
M. J. Brennan and Y. Xia, Dynamic asset allocation under inflation, Journal of Finance, 57 (2002), 12011238. doi: 10.1111/15406261.00459. 
[4] 
T. Chellathurai and T. Draviam, Dynamic portfolio selection with fixed and/or proportional transaction costs using nonsingular stochastic optimal control theory, Journal of Economic Dynamics and Control, 31 (2007), 21682195. doi: 10.1016/j.jedc.2006.06.006. 
[5] 
P. Chen, H. L. Yang and G. Yin, Markowitz's meanvariance assetliability management with regime switching: A continuoustime model, Insurance: Mathematics and Economics, 43 (2008), 456465. doi: 10.1016/j.insmatheco.2008.09.001. 
[6] 
Y. Y. Chou, N. W. Han and M. W. Hung, Optimal portfolioconsumption choice under stochastic inflation with nominal and indexed bonds, Applied Stochastic Models in Business and Industry, 27 (2011), 691706. doi: 10.1002/asmb.886. 
[7] 
O. L. V. Costa and A. D. Oliveira, Optimal meanvariance control for discretetime linear systems with Markovian jumps and multiplicative noises, Automatica, 48 (2012), 304315. doi: 10.1016/j.automatica.2011.11.009. 
[8] 
R. Ferland and F. Watier, Meanvariance efficiency with extended CIR interest rates, Applied Stochastic Models in Business and Industry, 26 (2010), 7184. 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. Larilavassani and X. Li, Dynamic meanvariance portfolio selection with borrowing constraint, European Journal of Operational Research, 200 (2010), 313319. 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), 11591164. 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), 97117. doi: 10.1007/s1047900805099. 
[13] 
N. W. Han and M. W. Hung, Optimal asset allocation for DC pension plans under inflation, Insurance: Mathematics and Economics, 51 (2012), 172181. doi: 10.1016/j.insmatheco.2012.03.003. 
[14] 
R. JosaFombellida and J. P. RincónZapatero, Optimal asset allocation for aggregated defined benefit pension funds with stochastic interest rates, European Journal of Operational Research, 201 (2010), 211221. 
[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), 12501269. doi: 10.1137/S0363012900377791. 
[16] 
P. Lakner and L. M. Nygren, Portfolio optimization with downside constraints, Mathematical Finance, 16 (2006), 283299. doi: 10.1111/j.14679965.2006.00272.x. 
[17] 
M. Leippold, F. Trojani and P. Vanini, Multiperiod meanvariance efficient portfolios with endogenous liabilities, Quantitative Finance, 11 (2011), 15351546. doi: 10.1080/14697680902950813. 
[18] 
D. Li and W. L. Ng, Optimal dynamic portfolio selection: Multiperiod meanvariance formulation, Mathematical Finance, 10 (2000), 387406. 
[19] 
X. Li and X. Y. Zhou, Continuoustime meanvariance efficiency: The 80 The Annals of Applied Probability, 16 (2006), 17511763. doi: 10.1214/105051606000000349. 
[20] 
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. 
[21] 
A. E. B. Lim and X. Y. Zhou, Meanvariance portfolio selection with random parameters in a complete market, Mathematics of Operations Research, 27 (2002), 101120. 
[22] 
D. G. Luenberger, Optimization by Vector Space Methods, Wiley, New York, 1969. 
[23] 
H. Markowitz, Portfolio selection, Journal of Finance, 7 (1952), 7791. 
[24] 
R. C. Merton, Lifetime portfolio selection under uncertainty: The continuoustime model, Review of Economic and Statistics, 51 (1969), 247256. 
[25] 
C. Munk and C. Sørensen, Optimal consumption and investment strategies with stochastic interest rates, Journal of Banking & Finance, 28 (2004), 19872013. 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), 433462. doi: 10.1016/j.jfineco.2010.01.004. 
[27] 
C. Munk and C. Sørensen and T. N. Vinther, Dynamic asset allocation under meanreverting returns, stochastic interest rates, and inflation uncertainty: Are popular recommendations consistent with rational behavior?, International Review of Economics and Finance, 13 (2004), 141166. 
[28] 
P. A. Samuelson, Lifetime portfolio selection by dynamic stochastic programming, Review of Economics and Statistics, 51 (1969), 239246. doi: 10.2307/1926559. 
[29] 
Z. Wang and S. Y. Liu, Multiperiod meanvariance portfolio selection with fixed and proportional transaction costs, Journal of Industrial and Management Optimization, 9 (2013), 643657. doi: 10.3934/jimo.2013.9.643. 
[30] 
H. L. Wu, Meanvariance portfolio selection with a stochastic cash flow in a markovswitching jumpdiffusion market, Journal of Optimization Theory and Applications, 158 (2013), 918934. doi: 10.1007/s109570130292x. 
[31] 
H. X. Yao, Y. Z. Lai and Y. Li, Continuoustime meanvariance assetliability management with endogenous liabilities, Insurance: Mathematics and Economics, 52 (2013), 617. doi: 10.1016/j.insmatheco.2012.10.001. 
[32] 
H. X. Yao, Y. Z. Lai and Z. F. Hao, Uncertain exit time multiperiod meanvariance portfolio selection with endogenous liabilities and Markov jumps, Automatica, 49 (2013), 32583269. doi: 10.1016/j.automatica.2013.08.023. 
[33] 
L. Yi, Z. F. Li and D. Li, Mutliperiod portfolio selection for assetliability management with uncertain investment horizon, Journal of Industrial and Management Optimization, 4 (2008), 535552. 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), 405409. 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), 353369. doi: 10.1007/s0018600902945. 
[36] 
Y. Zeng, Z. F. Li and J. J. Liu, Optimal Strategies Of Benchmark And MeanVariance Portfolio Selection Problems For Insurers, Journal of Industrial and Management Optimization, 6 (2010), 483496. doi: 10.3934/jimo.2010.6.483. 
[37] 
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. 
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