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OPTIMAL PORTFOLIO AND CONSUMPTION MODELS UNDER LOSS AVERSION IN INFINITE TIME HORIZON

Published online by Cambridge University Press:  14 June 2016

Jingjing Song ,
Xiuchun Bi  and
Shuguang Zhang
Jingjing Song
Affiliation:
School of Mathematical Sciences, Xiamen University, Xiamen, Fujian 361005, People's Republic of China
Xiuchun Bi
Affiliation:
Department of Statistic and Finance, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China E-mail: xcbi@mail.ustc.edu.cn, bxcqfnu@163.com
Shuguang Zhang
Affiliation:
Department of Statistic and Finance, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China E-mail: xcbi@mail.ustc.edu.cn, bxcqfnu@163.com
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Abstract

This paper investigates continuous-time optimal portfolio and consumption problems under loss aversion in an infinite time horizon. The investor's goal is to choose the optimal portfolio and consumption policies to maximize total discounted S-shaped utility from consumption. The problems are solved under two different situations respectively for the reference level: exogenous or endogenous. For the case of exogenous reference level, which is independent of the consumption policy, the optimal consumption policy and wealth process are obtained through the martingale method and replicating technique. For the case of endogenous reference level, which is related to the past actual consumption, the optimization problem with stochastic reference level is first transformed into an equivalent optimization problem with zero reference point, the corresponding relationship between them is proved, and then the relevant optimal consumption policy and wealth process are also obtained. When the investment opportunity sets are constants, the closed-form solutions of the portfolio and consumption policies are derived under two different situations respectively.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 30 , Issue 4 , October 2016 , pp. 553 - 575
Copyright
Copyright © Cambridge University Press 2016 

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References

1. Benartzi, S. & Thaler, R. (1995). Myopic loss aversion and the equity premium puzzle. Quarterly Journal of Economics 110: 73–92.Google Scholar
2. Berkelaar, A., Kouwenberg, R., & Post, T. (2004). Optimal portfolio choice under loss aversion. The Review of Economics and Statistics 86(4): 973–987.Google Scholar
3. Bowman, D., Minehart, D., & Rabin, M. (1999). Loss aversion in a consumption-savings model. Journal of Economic Behavior and Organization 38: 155–178.Google Scholar
4. Camerer, C. (1995). Individual decision making. In Kagel, J.H. & Roth, A.E. (eds.), The handbook of experimental economics. Princeton: Princeton University Press, pp. 587–703.Google Scholar
5. Jin, H. & Zhou, X.Y. (2008). Behavioral portfolio selection in continuous time. Mathematical Finance 18(3): 385–426.CrossRefGoogle Scholar
6. Kahneman, D. & Tversky, A. (1979). Prospect theory-analysis of decision under risk. Econometrica 47(2): 263–291.Google Scholar
7. Kahneman, D., Knetsch, J., & Thaler, R. (1991). Anomalies: the endowment effect, loss aversion, and status quo bias. Journal of Economic Perspectives 5(1): 193–206.Google Scholar
8. Karatzas, I. & Shreve, S. (1998). Methods of mathematical finance. New York: Springer-Verlag.Google Scholar
9. Koszegi, B. & Rabin, M. (2006). A model of reference-dependent preferences. The Quarterly Journal of Economics 121(4): 1133–1165.Google Scholar
10. Koszegi, B. & Rabin, M. (2007). Reference-dependent risk attitudes. The American Economic Review 97(4): 1047–1073.CrossRefGoogle Scholar
11. Merton, R.C. (1969). Lifetime portfolio selection under uncertainty: the continuous-time case. The Review of Economics and Statistics 51(3): 247–257.Google Scholar
12. Mi, H., Bi, X.C., & Zhang, S.G. (2015). Dynamic asset allocation with loss aversion in a jump-diffusion model. Acta Mathematicae Applicatae Sinica, English Series 31(2): 557–566.Google Scholar
13. Samuelson, W. & Zeckhauser, R. (1988). Status quo bias in decision making. Journal of Risk and Uncertainty 1: 7–59.CrossRefGoogle Scholar
14. Schroder, M. & Skiadas, C. (2002). An isomorphism between asset pricing models with and without linear habit formation. Review of Financial Studies 15(4): 1189–1221.Google Scholar
15. Thaler, R. (1980). Toward a positive theory of consumer choice. Journal of Economic Behavior and Organization 1: 39–60.Google Scholar
16. Tversky, A. & Kahneman, D. (1991). Loss aversion in riskless choice: a reference dependent model. Quarterly Journal of Economics 106: 1039–1061.Google Scholar
17. Tversky, A. & Kahneman, D. (1992). Advances in prospect theory – cumulative representation of uncertainty. Journal of Risk and Uncertainty 5(4): 297–323.CrossRefGoogle Scholar
18. Zhang, S., Jin, H.Q., & Zhou, X.Y. (2011). Behavioral portfolio selection with loss control. Acta Mathematica Sinica, English Series 27(2): 255–274.CrossRefGoogle Scholar