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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: [email protected], [email protected]
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: [email protected], [email protected]
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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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