# American Institute of Mathematical Sciences

January  2011, 7(1): 139-156. doi: 10.3934/jimo.2011.7.139

## Optimal consumption and investment under irrational beliefs

 1 School of Business and Management, Hong Kong University of Science and Technology, Hong Kong, China 2 School of Economics and Management, Tsinghua University, Beijing, China

Received  March 2010 Revised  October 2010 Published  January 2011

In this paper, we study how irrationality affects the investor's consumption and investment decisions. We build a continuous-time financial model, where an irrational investor determines his consumption and investment according to an exogenous price process. The main results are as follows. First, compared with a rational investor, an optimistic irrational investor tends to consume more, while a pessimistic irrational investor tends to consume less. Second, the more irrational the investor, the more volatile his consumption. Third, the extremely irrational investor can get more ex ante expected utility than his rational counterpart, no matter he is optimistic or pessimistic.
Citation: Lei Sun, Lihong Zhang. Optimal consumption and investment under irrational beliefs. Journal of Industrial & Management Optimization, 2011, 7 (1) : 139-156. doi: 10.3934/jimo.2011.7.139
##### References:

show all references

##### References:
 [1] Zuo Quan Xu, Fahuai Yi. An optimal consumption-investment model with constraint on consumption. Mathematical Control & Related Fields, 2016, 6 (3) : 517-534. doi: 10.3934/mcrf.2016014 [2] Jingzhen Liu, Ka-Fai Cedric Yiu, Kok Lay Teo. Optimal investment-consumption problem with constraint. Journal of Industrial & Management Optimization, 2013, 9 (4) : 743-768. doi: 10.3934/jimo.2013.9.743 [3] Jiaqin Wei, Danping Li, Yan Zeng. Robust optimal consumption-investment strategy with non-exponential discounting. Journal of Industrial & Management Optimization, 2020, 16 (1) : 207-230. doi: 10.3934/jimo.2018147 [4] Min Dai, Zhou Yang. A note on finite horizon optimal investment and consumption with transaction costs. Discrete & Continuous Dynamical Systems - B, 2016, 21 (5) : 1445-1454. doi: 10.3934/dcdsb.2016005 [5] 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) : 1937-1953. doi: 10.3934/jimo.2018130 [6] Ka Chun Cheung, Hailiang Yang. Optimal investment-consumption strategy in a discrete-time model with regime switching. Discrete & Continuous Dynamical Systems - B, 2007, 8 (2) : 315-332. doi: 10.3934/dcdsb.2007.8.315 [7] Qian Zhao, Rongming Wang, Jiaqin Wei. Time-inconsistent consumption-investment problem for a member in a defined contribution pension plan. Journal of Industrial & Management Optimization, 2016, 12 (4) : 1557-1585. doi: 10.3934/jimo.2016.12.1557 [8] Jiapeng Liu, Ruihua Liu, Dan Ren. Investment and consumption in regime-switching models with proportional transaction costs and log utility. Mathematical Control & Related Fields, 2017, 7 (3) : 465-491. doi: 10.3934/mcrf.2017017 [9] Nan Zhang, Ping Chen, Zhuo Jin, Shuanming Li. Markowitz's mean-variance optimization with investment and constrained reinsurance. Journal of Industrial & Management Optimization, 2017, 13 (1) : 375-397. doi: 10.3934/jimo.2016022 [10] Yang Shen, Tak Kuen Siu. Consumption-portfolio optimization and filtering in a hidden Markov-modulated asset price model. Journal of Industrial & Management Optimization, 2017, 13 (1) : 23-46. doi: 10.3934/jimo.2016002 [11] Dongping Zhuang. Irrational stable commutator length in finitely presented groups. Journal of Modern Dynamics, 2008, 2 (3) : 499-507. doi: 10.3934/jmd.2008.2.499 [12] Ferrán Valdez. Veech groups, irrational billiards and stable abelian differentials. Discrete & Continuous Dynamical Systems, 2012, 32 (3) : 1055-1063. doi: 10.3934/dcds.2012.32.1055 [13] W. Patrick Hooper. Lower bounds on growth rates of periodic billiard trajectories in some irrational polygons. Journal of Modern Dynamics, 2007, 1 (4) : 649-663. doi: 10.3934/jmd.2007.1.649 [14] Marie-Claude Arnaud. A nondifferentiable essential irrational invariant curve for a $C^1$ symplectic twist map. Journal of Modern Dynamics, 2011, 5 (3) : 583-591. doi: 10.3934/jmd.2011.5.583 [15] Hans Koch. On trigonometric skew-products over irrational circle-rotations. Discrete & Continuous Dynamical Systems, 2021, 41 (11) : 5455-5471. doi: 10.3934/dcds.2021084 [16] Stefano Galatolo, Alfonso Sorrentino. Quantitative statistical stability and linear response for irrational rotations and diffeomorphisms of the circle. Discrete & Continuous Dynamical Systems, 2021  doi: 10.3934/dcds.2021138 [17] Fengjun Wang, Qingling Zhang, Bin Li, Wanquan Liu. Optimal investment strategy on advertisement in duopoly. Journal of Industrial & Management Optimization, 2016, 12 (2) : 625-636. doi: 10.3934/jimo.2016.12.625 [18] Xin Jiang, Kam Chuen Yuen, Mi Chen. Optimal investment and reinsurance with premium control. Journal of Industrial & Management Optimization, 2020, 16 (6) : 2781-2797. doi: 10.3934/jimo.2019080 [19] Ming Yang, Chulin Li. Valuing investment project in competitive environment. Conference Publications, 2003, 2003 (Special) : 945-950. doi: 10.3934/proc.2003.2003.945 [20] Adrien Nguyen Huu. Investment under uncertainty, competition and regulation. Journal of Dynamics & Games, 2014, 1 (4) : 579-598. doi: 10.3934/jdg.2014.1.579

2020 Impact Factor: 1.801