
Previous Article
A semidiscrete Galerkin scheme for backward stochastic parabolic differential equations
 MCRF Home
 This Issue
 Next Article
An optimal consumptioninvestment model with constraint on consumption
1.  Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong 
2.  School of Finance, Guangdong University of Foreign Studies, Guangzhou 510420, China 
References:
[1] 
M. Akian, J. L. Menaldi and A. Sulem, On an investmentconsumption model with transaction costs,, SIAM Journal on Control and Optimization, 34 (1996), 329. doi: 10.1137/S0363012993247159. Google Scholar 
[2] 
I. Bardhan, Consumption and investment under constraints,, Journal of Economic Dynamics and Control, 18 (1994), 909. Google Scholar 
[3] 
X. S. Chen and F. H. Yi, A problem of singular stochastic control with optimal stopping in finite horizon,, SIAM Journal on Control and Optimization, 50 (2012), 2151. doi: 10.1137/110832264. Google Scholar 
[4] 
M. G. Crandall and P. L. Lions, Viscosity solutions of HamiltonJacobi equations,, Trans. AMS, 277 (1983), 1. doi: 10.1090/S00029947198306900398. Google Scholar 
[5] 
J. Cvitanić and I. Karatzas, Convex duality in constrained portfolio optimization,, Annals of Applied Probability, 2 (1992), 767. doi: 10.1214/aoap/1177005576. Google Scholar 
[6] 
J. Cvitanić and I. Karatzas, Hedging contingent claims with constrained portfolios,, Annals of Applied Probability, 3 (1993), 652. doi: 10.1214/aoap/1177005357. Google Scholar 
[7] 
M. Dai and Z. Xu, Optimal redeeming strategy of stock loans with finite maturity,, Mathematical Finance, 21 (2011), 775. doi: 10.1111/j.14679965.2010.00449.x. Google Scholar 
[8] 
M. Dai, Z. Q. Xu and X. Y. Zhou, Continuoustime meanvariance portfolio selection with proportional transaction costs,, SIAM Journal on Financial Mathematics, 1 (2010), 96. doi: 10.1137/080742889. Google Scholar 
[9] 
M. Dai and F. H. Yi, Finite horizon optimal investment with transaction costs: A parabolic double obstacle problem,, Journal of Differential Equations, 246 (2009), 1445. doi: 10.1016/j.jde.2008.11.003. Google Scholar 
[10] 
M. H. A. Davis and A. Norman, Portfolio selection with transaction costs,, Mathematics of Operations Research, 15 (1990), 676. doi: 10.1287/moor.15.4.676. Google Scholar 
[11] 
R. Elie and N. Touzi, Optimal lifetime consumption and investment under a drawdown constraint,, Finance and Stochastics, 12 (2008), 299. doi: 10.1007/s0078000800668. Google Scholar 
[12] 
W. H. Fleming and H. M. Soner, Controlled Markov Processes and Viscosity Solutions,, Second edition. Stochastic Modelling and Applied Probability, (2006). Google Scholar 
[13] 
W. H. Fleming and T. Zariphopoulou, An optimal consumption and investment models with borrowing constraints,, Mathematics of Operations Research, 16 (1991), 802. doi: 10.1287/moor.16.4.802. Google Scholar 
[14] 
P. L. Lions, Optimal control of diffusion processes and HamiltonJacobiBellman equations, Part 2,, Communications in Partial Differential Equations, 8 (1983), 1229. doi: 10.1080/03605308308820301. Google Scholar 
[15] 
H. Markowitz, Portfolio selection,, Journal of Finance, 7 (1952), 77. doi: 10.1111/j.15406261.1952.tb01525.x. Google Scholar 
[16] 
H. Markowitz, Portfolio Selection: Efficient Diversification of Investments,, John Wiley & Sons, (1959). Google Scholar 
[17] 
R. C. Merton, Lifetime portfolio selection under uncertainty: The continuoustime case,, Review of Economics and Statistics, 51 (1969), 247. doi: 10.2307/1926560. Google Scholar 
[18] 
R. C. Merton, Optimum consumption and portfolio rules in a continuous time model,, Journal of Economic Theory, 3 (1971), 373. doi: 10.1016/00220531(71)90038X. Google Scholar 
[19] 
R. C. Merton, Theory of finance from the perspective of continuous time,, Journal of Financial and Quantitative Analysis, 10 (1975), 659. doi: 10.2307/2330617. Google Scholar 
[20] 
P. A. Samuelson, Lifetime portfolio selection by dynamic stochastic programming,, Review of Economics and Statistics, 51 (1969), 239. Google Scholar 
[21] 
P. S. Sethi, Optimal Consumption and Investment with Bankruptcy,, Kluwer Academic Publishers, (1997). doi: 10.1007/9781461562573. Google Scholar 
[22] 
S. Shreve and M. Soner, Optimal investment and consumption with transaction costs,, Annals of Applied Probability, 4 (1994), 609. doi: 10.1214/aoap/1177004966. Google Scholar 
[23] 
T. Zariphopoulou, Investmentconsumption models with transaction fees and Markov chain parameters,, SIAM Journal on Control and Optimization, 30 (1992), 613. doi: 10.1137/0330035. Google Scholar 
[24] 
T. Zariphopoulou, Consumptioninvestment models with constraints,, SIAM Journal on Control and Optimization, 32 (1994), 59. doi: 10.1137/S0363012991218827. Google Scholar 
show all references
References:
[1] 
M. Akian, J. L. Menaldi and A. Sulem, On an investmentconsumption model with transaction costs,, SIAM Journal on Control and Optimization, 34 (1996), 329. doi: 10.1137/S0363012993247159. Google Scholar 
[2] 
I. Bardhan, Consumption and investment under constraints,, Journal of Economic Dynamics and Control, 18 (1994), 909. Google Scholar 
[3] 
X. S. Chen and F. H. Yi, A problem of singular stochastic control with optimal stopping in finite horizon,, SIAM Journal on Control and Optimization, 50 (2012), 2151. doi: 10.1137/110832264. Google Scholar 
[4] 
M. G. Crandall and P. L. Lions, Viscosity solutions of HamiltonJacobi equations,, Trans. AMS, 277 (1983), 1. doi: 10.1090/S00029947198306900398. Google Scholar 
[5] 
J. Cvitanić and I. Karatzas, Convex duality in constrained portfolio optimization,, Annals of Applied Probability, 2 (1992), 767. doi: 10.1214/aoap/1177005576. Google Scholar 
[6] 
J. Cvitanić and I. Karatzas, Hedging contingent claims with constrained portfolios,, Annals of Applied Probability, 3 (1993), 652. doi: 10.1214/aoap/1177005357. Google Scholar 
[7] 
M. Dai and Z. Xu, Optimal redeeming strategy of stock loans with finite maturity,, Mathematical Finance, 21 (2011), 775. doi: 10.1111/j.14679965.2010.00449.x. Google Scholar 
[8] 
M. Dai, Z. Q. Xu and X. Y. Zhou, Continuoustime meanvariance portfolio selection with proportional transaction costs,, SIAM Journal on Financial Mathematics, 1 (2010), 96. doi: 10.1137/080742889. Google Scholar 
[9] 
M. Dai and F. H. Yi, Finite horizon optimal investment with transaction costs: A parabolic double obstacle problem,, Journal of Differential Equations, 246 (2009), 1445. doi: 10.1016/j.jde.2008.11.003. Google Scholar 
[10] 
M. H. A. Davis and A. Norman, Portfolio selection with transaction costs,, Mathematics of Operations Research, 15 (1990), 676. doi: 10.1287/moor.15.4.676. Google Scholar 
[11] 
R. Elie and N. Touzi, Optimal lifetime consumption and investment under a drawdown constraint,, Finance and Stochastics, 12 (2008), 299. doi: 10.1007/s0078000800668. Google Scholar 
[12] 
W. H. Fleming and H. M. Soner, Controlled Markov Processes and Viscosity Solutions,, Second edition. Stochastic Modelling and Applied Probability, (2006). Google Scholar 
[13] 
W. H. Fleming and T. Zariphopoulou, An optimal consumption and investment models with borrowing constraints,, Mathematics of Operations Research, 16 (1991), 802. doi: 10.1287/moor.16.4.802. Google Scholar 
[14] 
P. L. Lions, Optimal control of diffusion processes and HamiltonJacobiBellman equations, Part 2,, Communications in Partial Differential Equations, 8 (1983), 1229. doi: 10.1080/03605308308820301. Google Scholar 
[15] 
H. Markowitz, Portfolio selection,, Journal of Finance, 7 (1952), 77. doi: 10.1111/j.15406261.1952.tb01525.x. Google Scholar 
[16] 
H. Markowitz, Portfolio Selection: Efficient Diversification of Investments,, John Wiley & Sons, (1959). Google Scholar 
[17] 
R. C. Merton, Lifetime portfolio selection under uncertainty: The continuoustime case,, Review of Economics and Statistics, 51 (1969), 247. doi: 10.2307/1926560. Google Scholar 
[18] 
R. C. Merton, Optimum consumption and portfolio rules in a continuous time model,, Journal of Economic Theory, 3 (1971), 373. doi: 10.1016/00220531(71)90038X. Google Scholar 
[19] 
R. C. Merton, Theory of finance from the perspective of continuous time,, Journal of Financial and Quantitative Analysis, 10 (1975), 659. doi: 10.2307/2330617. Google Scholar 
[20] 
P. A. Samuelson, Lifetime portfolio selection by dynamic stochastic programming,, Review of Economics and Statistics, 51 (1969), 239. Google Scholar 
[21] 
P. S. Sethi, Optimal Consumption and Investment with Bankruptcy,, Kluwer Academic Publishers, (1997). doi: 10.1007/9781461562573. Google Scholar 
[22] 
S. Shreve and M. Soner, Optimal investment and consumption with transaction costs,, Annals of Applied Probability, 4 (1994), 609. doi: 10.1214/aoap/1177004966. Google Scholar 
[23] 
T. Zariphopoulou, Investmentconsumption models with transaction fees and Markov chain parameters,, SIAM Journal on Control and Optimization, 30 (1992), 613. doi: 10.1137/0330035. Google Scholar 
[24] 
T. Zariphopoulou, Consumptioninvestment models with constraints,, SIAM Journal on Control and Optimization, 32 (1994), 59. doi: 10.1137/S0363012991218827. Google Scholar 
[1] 
Jiaqin Wei, Danping Li, Yan Zeng. Robust optimal consumptioninvestment strategy with nonexponential discounting. Journal of Industrial & Management Optimization, 2017, 13 (5) : 124. doi: 10.3934/jimo.2018147 
[2] 
Jingzhen Liu, KaFai Cedric Yiu, Kok Lay Teo. Optimal investmentconsumption problem with constraint. Journal of Industrial & Management Optimization, 2013, 9 (4) : 743768. doi: 10.3934/jimo.2013.9.743 
[3] 
Qian Zhao, Rongming Wang, Jiaqin Wei. Timeinconsistent consumptioninvestment problem for a member in a defined contribution pension plan. Journal of Industrial & Management Optimization, 2016, 12 (4) : 15571585. doi: 10.3934/jimo.2016.12.1557 
[4] 
Chonghu Guan, Xun Li, Zuo Quan Xu, Fahuai Yi. A stochastic control problem and related free boundaries in finance. Mathematical Control & Related Fields, 2017, 7 (4) : 563584. doi: 10.3934/mcrf.2017021 
[5] 
Lei Sun, Lihong Zhang. Optimal consumption and investment under irrational beliefs. Journal of Industrial & Management Optimization, 2011, 7 (1) : 139156. doi: 10.3934/jimo.2011.7.139 
[6] 
Yuan Tan, Qingyuan Cao, Lan Li, Tianshi Hu, Min Su. A chanceconstrained stochastic model predictive control problem with disturbance feedback. Journal of Industrial & Management Optimization, 2017, 13 (5) : 113. doi: 10.3934/jimo.2019099 
[7] 
Ka Chun Cheung, Hailiang Yang. Optimal investmentconsumption strategy in a discretetime model with regime switching. Discrete & Continuous Dynamical Systems  B, 2007, 8 (2) : 315332. doi: 10.3934/dcdsb.2007.8.315 
[8] 
Min Dai, Zhou Yang. A note on finite horizon optimal investment and consumption with transaction costs. Discrete & Continuous Dynamical Systems  B, 2016, 21 (5) : 14451454. doi: 10.3934/dcdsb.2016005 
[9] 
Yong Ma, Shiping Shan, Weidong Xu. Optimal investment and consumption in the market with jump risk and capital gains tax. Journal of Industrial & Management Optimization, 2019, 15 (4) : 19371953. doi: 10.3934/jimo.2018130 
[10] 
Ciro D'Apice, Peter I. Kogut, Rosanna Manzo. On relaxation of state constrained optimal control problem for a PDEODE model of supply chains. Networks & Heterogeneous Media, 2014, 9 (3) : 501518. doi: 10.3934/nhm.2014.9.501 
[11] 
Sören Bartels, Marijo Milicevic. Iterative finite element solution of a constrained total variation regularized model problem. Discrete & Continuous Dynamical Systems  S, 2017, 10 (6) : 12071232. doi: 10.3934/dcdss.2017066 
[12] 
Lili Chang, Wei Gong, Guiquan Sun, Ningning Yan. PDEconstrained optimal control approach for the approximation of an inverse Cauchy problem. Inverse Problems & Imaging, 2015, 9 (3) : 791814. doi: 10.3934/ipi.2015.9.791 
[13] 
Xiaoshan Chen, Fahuai Yi. Free boundary problem of Barenblatt equation in stochastic control. Discrete & Continuous Dynamical Systems  B, 2016, 21 (5) : 14211434. doi: 10.3934/dcdsb.2016003 
[14] 
Kazimierz Malanowski, Helmut Maurer. Sensitivity analysis for state constrained optimal control problems. Discrete & Continuous Dynamical Systems  A, 1998, 4 (2) : 241272. doi: 10.3934/dcds.1998.4.241 
[15] 
Sie Long Kek, Kok Lay Teo, Mohd Ismail Abd Aziz. Filtering solution of nonlinear stochastic optimal control problem in discretetime with modelreality differences. Numerical Algebra, Control & Optimization, 2012, 2 (1) : 207222. doi: 10.3934/naco.2012.2.207 
[16] 
Chonghu Guan, Fahuai Yi, Xiaoshan Chen. A fully nonlinear free boundary problem arising from optimal dividend and risk control model. Mathematical Control & Related Fields, 2019, 9 (3) : 425452. doi: 10.3934/mcrf.2019020 
[17] 
Shanjian Tang, Fu Zhang. Pathdependent optimal stochastic control and viscosity solution of associated Bellman equations. Discrete & Continuous Dynamical Systems  A, 2015, 35 (11) : 55215553. doi: 10.3934/dcds.2015.35.5521 
[18] 
Chengxia Lei, Yihong Du. Asymptotic profile of the solution to a free boundary problem arising in a shifting climate model. Discrete & Continuous Dynamical Systems  B, 2017, 22 (3) : 895911. doi: 10.3934/dcdsb.2017045 
[19] 
Shaoyong Lai, Qichang Xie. A selection problem for a constrained linear regression model. Journal of Industrial & Management Optimization, 2008, 4 (4) : 757766. doi: 10.3934/jimo.2008.4.757 
[20] 
Bin Li, Kok Lay Teo, ChengChew Lim, Guang Ren Duan. An optimal PID controller design for nonlinear constrained optimal control problems. Discrete & Continuous Dynamical Systems  B, 2011, 16 (4) : 11011117. doi: 10.3934/dcdsb.2011.16.1101 
2018 Impact Factor: 1.292
Tools
Metrics
Other articles
by authors
[Back to Top]