Robust optimal consumption-investment strategy with non-exponential discounting

Jiaqin Wei; Danping Li; Yan Zeng

doi:10.3934/jimo.2018147

Article Contents

2020, Volume 16, Issue 1: 207-230. Doi: 10.3934/jimo.2018147

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Robust optimal consumption-investment strategy with non-exponential discounting

1.
School of Statistics, East China Normal University, Shanghai, 200241, China
2.
Lingnan (University) College, Sun Yat-sen University, Guangzhou 510275, China

* Corresponding author
* Corresponding author

Received: July 2017

Revised: June 2018

Early access: September 2018

Published: October 2019

This work was supported by Program of Shanghai Subject Chief Scientist (14XD1401600), the 111 Project (B14019), National Natural Science Foundation of China (11771466, 11601157, 11231005, 71571195, 71771220, 71721001, 11801179), Major Program of the National Social Science Foundation of China (No. 17ZDA073), Fok Ying Tung Education Foundation for Young Teachers in the Higher Education Institutions of China (151081), Guangdong Natural Science Foundation for Research Team (2014A030312003), Guangdong Natural Science Foundation for Distinguished Young Scholar (2015A030306040), and Fundamental Research Funds for the Central Universities (No. 17wkzd08).

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Abstract

This paper extends the existing dynamic consumption-investment problem to the case with more general discount functions under the robust framework. The decision-maker is ambiguity-averse and invests her wealth in a risk-free asset and a risky asset. Since non-exponential discounting is considered in our model, our optimization problem is time inconsistent. By solving the extended Hamilton-Jacobi-Bellman equations, the corresponding optimal consumption-investment strategies for sophisticated and naive investors under power and logarithmic utility functions are derived explicitly. Our model and results extend some existing ones and derive some interesting phenomena.

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Mathematics Subject Classification: Primary: 90B50, 93E20; Secondary: 91G80.

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Figure 1. Effects of $\eta$ on optimal proportion of wealth to consume and optimal value function

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