- Previous Article
- MCRF Home
- This Issue
-
Next Article
A semidiscrete Galerkin scheme for backward stochastic parabolic differential equations
An optimal consumption-investment 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 investment-consumption model with transaction costs, SIAM Journal on Control and Optimization, 34 (1996), 329-364.
doi: 10.1137/S0363012993247159. |
[2] |
I. Bardhan, Consumption and investment under constraints, Journal of Economic Dynamics and Control, 18 (1994), 909-929. |
[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), 2151-2172.
doi: 10.1137/110832264. |
[4] |
M. G. Crandall and P. L. Lions, Viscosity solutions of Hamilton-Jacobi equations, Trans. AMS, 277 (1983), 1-42.
doi: 10.1090/S0002-9947-1983-0690039-8. |
[5] |
J. Cvitanić and I. Karatzas, Convex duality in constrained portfolio optimization, Annals of Applied Probability, 2 (1992), 767-818.
doi: 10.1214/aoap/1177005576. |
[6] |
J. Cvitanić and I. Karatzas, Hedging contingent claims with constrained portfolios, Annals of Applied Probability, 3 (1993), 652-681.
doi: 10.1214/aoap/1177005357. |
[7] |
M. Dai and Z. Xu, Optimal redeeming strategy of stock loans with finite maturity, Mathematical Finance, 21 (2011), 775-793.
doi: 10.1111/j.1467-9965.2010.00449.x. |
[8] |
M. Dai, Z. Q. Xu and X. Y. Zhou, Continuous-time mean-variance portfolio selection with proportional transaction costs, SIAM Journal on Financial Mathematics, 1 (2010), 96-125.
doi: 10.1137/080742889. |
[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), 1445-1469.
doi: 10.1016/j.jde.2008.11.003. |
[10] |
M. H. A. Davis and A. Norman, Portfolio selection with transaction costs, Mathematics of Operations Research, 15 (1990), 676-713.
doi: 10.1287/moor.15.4.676. |
[11] |
R. Elie and N. Touzi, Optimal lifetime consumption and investment under a drawdown constraint, Finance and Stochastics, 12 (2008), 299-330.
doi: 10.1007/s00780-008-0066-8. |
[12] |
W. H. Fleming and H. M. Soner, Controlled Markov Processes and Viscosity Solutions, Second edition. Stochastic Modelling and Applied Probability, 25. Springer, New York, 2006. |
[13] |
W. H. Fleming and T. Zariphopoulou, An optimal consumption and investment models with borrowing constraints, Mathematics of Operations Research, 16 (1991), 802-822.
doi: 10.1287/moor.16.4.802. |
[14] |
P. L. Lions, Optimal control of diffusion processes and Hamilton-Jacobi-Bellman equations, Part 2, Communications in Partial Differential Equations, 8 (1983), 1229-1276.
doi: 10.1080/03605308308820301. |
[15] |
H. Markowitz, Portfolio selection, Journal of Finance, 7 (1952), 77-91.
doi: 10.1111/j.1540-6261.1952.tb01525.x. |
[16] |
H. Markowitz, Portfolio Selection: Efficient Diversification of Investments, John Wiley & Sons, New York, 1959. |
[17] |
R. C. Merton, Lifetime portfolio selection under uncertainty: The continuous-time case, Review of Economics and Statistics, 51 (1969), 247-257.
doi: 10.2307/1926560. |
[18] |
R. C. Merton, Optimum consumption and portfolio rules in a continuous time model, Journal of Economic Theory, 3 (1971), 373-413.
doi: 10.1016/0022-0531(71)90038-X. |
[19] |
R. C. Merton, Theory of finance from the perspective of continuous time, Journal of Financial and Quantitative Analysis, 10 (1975), 659-674.
doi: 10.2307/2330617. |
[20] |
P. A. Samuelson, Lifetime portfolio selection by dynamic stochastic programming, Review of Economics and Statistics, 51 (1969), 239-246. |
[21] |
P. S. Sethi, Optimal Consumption and Investment with Bankruptcy, Kluwer Academic Publishers, Norwell, MA, 1997.
doi: 10.1007/978-1-4615-6257-3. |
[22] |
S. Shreve and M. Soner, Optimal investment and consumption with transaction costs, Annals of Applied Probability, 4 (1994), 609-692.
doi: 10.1214/aoap/1177004966. |
[23] |
T. Zariphopoulou, Investment-consumption models with transaction fees and Markov chain parameters, SIAM Journal on Control and Optimization, 30 (1992), 613-636.
doi: 10.1137/0330035. |
[24] |
T. Zariphopoulou, Consumption-investment models with constraints, SIAM Journal on Control and Optimization, 32 (1994), 59-85.
doi: 10.1137/S0363012991218827. |
show all references
References:
[1] |
M. Akian, J. L. Menaldi and A. Sulem, On an investment-consumption model with transaction costs, SIAM Journal on Control and Optimization, 34 (1996), 329-364.
doi: 10.1137/S0363012993247159. |
[2] |
I. Bardhan, Consumption and investment under constraints, Journal of Economic Dynamics and Control, 18 (1994), 909-929. |
[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), 2151-2172.
doi: 10.1137/110832264. |
[4] |
M. G. Crandall and P. L. Lions, Viscosity solutions of Hamilton-Jacobi equations, Trans. AMS, 277 (1983), 1-42.
doi: 10.1090/S0002-9947-1983-0690039-8. |
[5] |
J. Cvitanić and I. Karatzas, Convex duality in constrained portfolio optimization, Annals of Applied Probability, 2 (1992), 767-818.
doi: 10.1214/aoap/1177005576. |
[6] |
J. Cvitanić and I. Karatzas, Hedging contingent claims with constrained portfolios, Annals of Applied Probability, 3 (1993), 652-681.
doi: 10.1214/aoap/1177005357. |
[7] |
M. Dai and Z. Xu, Optimal redeeming strategy of stock loans with finite maturity, Mathematical Finance, 21 (2011), 775-793.
doi: 10.1111/j.1467-9965.2010.00449.x. |
[8] |
M. Dai, Z. Q. Xu and X. Y. Zhou, Continuous-time mean-variance portfolio selection with proportional transaction costs, SIAM Journal on Financial Mathematics, 1 (2010), 96-125.
doi: 10.1137/080742889. |
[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), 1445-1469.
doi: 10.1016/j.jde.2008.11.003. |
[10] |
M. H. A. Davis and A. Norman, Portfolio selection with transaction costs, Mathematics of Operations Research, 15 (1990), 676-713.
doi: 10.1287/moor.15.4.676. |
[11] |
R. Elie and N. Touzi, Optimal lifetime consumption and investment under a drawdown constraint, Finance and Stochastics, 12 (2008), 299-330.
doi: 10.1007/s00780-008-0066-8. |
[12] |
W. H. Fleming and H. M. Soner, Controlled Markov Processes and Viscosity Solutions, Second edition. Stochastic Modelling and Applied Probability, 25. Springer, New York, 2006. |
[13] |
W. H. Fleming and T. Zariphopoulou, An optimal consumption and investment models with borrowing constraints, Mathematics of Operations Research, 16 (1991), 802-822.
doi: 10.1287/moor.16.4.802. |
[14] |
P. L. Lions, Optimal control of diffusion processes and Hamilton-Jacobi-Bellman equations, Part 2, Communications in Partial Differential Equations, 8 (1983), 1229-1276.
doi: 10.1080/03605308308820301. |
[15] |
H. Markowitz, Portfolio selection, Journal of Finance, 7 (1952), 77-91.
doi: 10.1111/j.1540-6261.1952.tb01525.x. |
[16] |
H. Markowitz, Portfolio Selection: Efficient Diversification of Investments, John Wiley & Sons, New York, 1959. |
[17] |
R. C. Merton, Lifetime portfolio selection under uncertainty: The continuous-time case, Review of Economics and Statistics, 51 (1969), 247-257.
doi: 10.2307/1926560. |
[18] |
R. C. Merton, Optimum consumption and portfolio rules in a continuous time model, Journal of Economic Theory, 3 (1971), 373-413.
doi: 10.1016/0022-0531(71)90038-X. |
[19] |
R. C. Merton, Theory of finance from the perspective of continuous time, Journal of Financial and Quantitative Analysis, 10 (1975), 659-674.
doi: 10.2307/2330617. |
[20] |
P. A. Samuelson, Lifetime portfolio selection by dynamic stochastic programming, Review of Economics and Statistics, 51 (1969), 239-246. |
[21] |
P. S. Sethi, Optimal Consumption and Investment with Bankruptcy, Kluwer Academic Publishers, Norwell, MA, 1997.
doi: 10.1007/978-1-4615-6257-3. |
[22] |
S. Shreve and M. Soner, Optimal investment and consumption with transaction costs, Annals of Applied Probability, 4 (1994), 609-692.
doi: 10.1214/aoap/1177004966. |
[23] |
T. Zariphopoulou, Investment-consumption models with transaction fees and Markov chain parameters, SIAM Journal on Control and Optimization, 30 (1992), 613-636.
doi: 10.1137/0330035. |
[24] |
T. Zariphopoulou, Consumption-investment models with constraints, SIAM Journal on Control and Optimization, 32 (1994), 59-85.
doi: 10.1137/S0363012991218827. |
[1] |
Jiaqin Wei, Danping Li, Yan Zeng. Robust optimal consumption-investment strategy with non-exponential discounting. Journal of Industrial and Management Optimization, 2020, 16 (1) : 207-230. doi: 10.3934/jimo.2018147 |
[2] |
Jingzhen Liu, Ka-Fai Cedric Yiu, Kok Lay Teo. Optimal investment-consumption problem with constraint. Journal of Industrial and Management Optimization, 2013, 9 (4) : 743-768. doi: 10.3934/jimo.2013.9.743 |
[3] |
Qian Zhao, Rongming Wang, Jiaqin Wei. Time-inconsistent consumption-investment problem for a member in a defined contribution pension plan. Journal of Industrial and Management Optimization, 2016, 12 (4) : 1557-1585. 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 and Related Fields, 2017, 7 (4) : 563-584. doi: 10.3934/mcrf.2017021 |
[5] |
Lei Sun, Lihong Zhang. Optimal consumption and investment under irrational beliefs. Journal of Industrial and Management Optimization, 2011, 7 (1) : 139-156. doi: 10.3934/jimo.2011.7.139 |
[6] |
Jingzhen Liu, Shiqi Yan, Shan Jiang, Jiaqin Wei. Optimal investment, consumption and life insurance strategies under stochastic differential utility with habit formation. Journal of Industrial and Management Optimization, 2022 doi: 10.3934/jimo.2022040 |
[7] |
Yuan Tan, Qingyuan Cao, Lan Li, Tianshi Hu, Min Su. A chance-constrained stochastic model predictive control problem with disturbance feedback. Journal of Industrial and Management Optimization, 2021, 17 (1) : 67-79. doi: 10.3934/jimo.2019099 |
[8] |
Ka Chun Cheung, Hailiang Yang. Optimal investment-consumption strategy in a discrete-time model with regime switching. Discrete and Continuous Dynamical Systems - B, 2007, 8 (2) : 315-332. doi: 10.3934/dcdsb.2007.8.315 |
[9] |
Min Dai, Zhou Yang. A note on finite horizon optimal investment and consumption with transaction costs. Discrete and Continuous Dynamical Systems - B, 2016, 21 (5) : 1445-1454. doi: 10.3934/dcdsb.2016005 |
[10] |
Yong Ma, Shiping Shan, Weidong Xu. Optimal investment and consumption in the market with jump risk and capital gains tax. Journal of Industrial and Management Optimization, 2019, 15 (4) : 1937-1953. doi: 10.3934/jimo.2018130 |
[11] |
Chonghu Guan, Xun Li, Rui Zhou, Wenxin Zhou. Free boundary problem for an optimal investment problem with a borrowing constraint. Journal of Industrial and Management Optimization, 2022, 18 (3) : 1915-1934. doi: 10.3934/jimo.2021049 |
[12] |
Ciro D'Apice, Peter I. Kogut, Rosanna Manzo. On relaxation of state constrained optimal control problem for a PDE-ODE model of supply chains. Networks and Heterogeneous Media, 2014, 9 (3) : 501-518. doi: 10.3934/nhm.2014.9.501 |
[13] |
Sören Bartels, Marijo Milicevic. Iterative finite element solution of a constrained total variation regularized model problem. Discrete and Continuous Dynamical Systems - S, 2017, 10 (6) : 1207-1232. doi: 10.3934/dcdss.2017066 |
[14] |
Lili Chang, Wei Gong, Guiquan Sun, Ningning Yan. PDE-constrained optimal control approach for the approximation of an inverse Cauchy problem. Inverse Problems and Imaging, 2015, 9 (3) : 791-814. doi: 10.3934/ipi.2015.9.791 |
[15] |
Xiaoshan Chen, Fahuai Yi. Free boundary problem of Barenblatt equation in stochastic control. Discrete and Continuous Dynamical Systems - B, 2016, 21 (5) : 1421-1434. doi: 10.3934/dcdsb.2016003 |
[16] |
Chonghu Guan, Fahuai Yi, Xiaoshan Chen. A fully nonlinear free boundary problem arising from optimal dividend and risk control model. Mathematical Control and Related Fields, 2019, 9 (3) : 425-452. doi: 10.3934/mcrf.2019020 |
[17] |
Kazimierz Malanowski, Helmut Maurer. Sensitivity analysis for state constrained optimal control problems. Discrete and Continuous Dynamical Systems, 1998, 4 (2) : 241-272. doi: 10.3934/dcds.1998.4.241 |
[18] |
Sie Long Kek, Kok Lay Teo, Mohd Ismail Abd Aziz. Filtering solution of nonlinear stochastic optimal control problem in discrete-time with model-reality differences. Numerical Algebra, Control and Optimization, 2012, 2 (1) : 207-222. doi: 10.3934/naco.2012.2.207 |
[19] |
Jingshi Li, Jiachuan Zhang, Guoliang Ju, Juntao You. A multi-mode expansion method for boundary optimal control problems constrained by random Poisson equations. Electronic Research Archive, 2020, 28 (2) : 977-1000. doi: 10.3934/era.2020052 |
[20] |
Chengxia Lei, Yihong Du. Asymptotic profile of the solution to a free boundary problem arising in a shifting climate model. Discrete and Continuous Dynamical Systems - B, 2017, 22 (3) : 895-911. doi: 10.3934/dcdsb.2017045 |
2021 Impact Factor: 1.141
Tools
Metrics
Other articles
by authors
[Back to Top]