Relative growth rate optimization under behavioral criterion

This paper studies a continuous-time optimal portfolio selection problem in a complete market for a behavioral investor whose preference is of the prospect type with probability distortion. The investor is concerned with the terminal relative growth rate (log-return) instead of absolute capital valu...

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Main Authors: Peng, Jing, Wei, Pengyu, Xu, Zuo Quan
Other Authors: Nanyang Business School
Format: Article
Language:English
Published: 2024
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Online Access:https://hdl.handle.net/10356/173743
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Institution: Nanyang Technological University
Language: English
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spelling sg-ntu-dr.10356-1737432024-02-26T05:38:28Z Relative growth rate optimization under behavioral criterion Peng, Jing Wei, Pengyu Xu, Zuo Quan Nanyang Business School Business and Management Behavioral finance Prospect theory This paper studies a continuous-time optimal portfolio selection problem in a complete market for a behavioral investor whose preference is of the prospect type with probability distortion. The investor is concerned with the terminal relative growth rate (log-return) instead of absolute capital value. This model can be regarded as an extension of the classical growth optimal problem to the behavioral framework. It leads to a new type of M-shaped utility maximization problem under nonlinear Choquet expectation. Due to the presence of probability distortion, the classical stochastic control methods are not applicable. Instead, we use the martingale method, concavification, and quantile optimization techniques to derive the closed-form optimal growth rate. We find that the benchmark growth rate has a significant impact on investment behaviors. Compared to S. Zhang, H. Q. Jin, and X. Zhou [Acta Math. Sin. (Engl. Ser.), 27 (2011), pp. 255-274] where the same preference measure is applied to the terminal relative wealth, we find a new phenomenon when the investor's risk tolerance level is high and the market state is bad. In addition, our optimal wealth in every scenario is less sensitive to the pricing kernel and thus more stable than theirs. 2024-02-26T05:38:28Z 2024-02-26T05:38:28Z 2023 Journal Article Peng, J., Wei, P. & Xu, Z. Q. (2023). Relative growth rate optimization under behavioral criterion. SIAM Journal On Financial Mathematics, 14(4), 1140-1174. https://dx.doi.org/10.1137/22M1496943 1945-497X https://hdl.handle.net/10356/173743 10.1137/22M1496943 2-s2.0-85179353915 4 14 1140 1174 en SIAM Journal on Financial Mathematics © 2023 Society for Industrial and Applied Mathematics. All rights reserved.
institution Nanyang Technological University
building NTU Library
continent Asia
country Singapore
Singapore
content_provider NTU Library
collection DR-NTU
language English
topic Business and Management
Behavioral finance
Prospect theory
spellingShingle Business and Management
Behavioral finance
Prospect theory
Peng, Jing
Wei, Pengyu
Xu, Zuo Quan
Relative growth rate optimization under behavioral criterion
description This paper studies a continuous-time optimal portfolio selection problem in a complete market for a behavioral investor whose preference is of the prospect type with probability distortion. The investor is concerned with the terminal relative growth rate (log-return) instead of absolute capital value. This model can be regarded as an extension of the classical growth optimal problem to the behavioral framework. It leads to a new type of M-shaped utility maximization problem under nonlinear Choquet expectation. Due to the presence of probability distortion, the classical stochastic control methods are not applicable. Instead, we use the martingale method, concavification, and quantile optimization techniques to derive the closed-form optimal growth rate. We find that the benchmark growth rate has a significant impact on investment behaviors. Compared to S. Zhang, H. Q. Jin, and X. Zhou [Acta Math. Sin. (Engl. Ser.), 27 (2011), pp. 255-274] where the same preference measure is applied to the terminal relative wealth, we find a new phenomenon when the investor's risk tolerance level is high and the market state is bad. In addition, our optimal wealth in every scenario is less sensitive to the pricing kernel and thus more stable than theirs.
author2 Nanyang Business School
author_facet Nanyang Business School
Peng, Jing
Wei, Pengyu
Xu, Zuo Quan
format Article
author Peng, Jing
Wei, Pengyu
Xu, Zuo Quan
author_sort Peng, Jing
title Relative growth rate optimization under behavioral criterion
title_short Relative growth rate optimization under behavioral criterion
title_full Relative growth rate optimization under behavioral criterion
title_fullStr Relative growth rate optimization under behavioral criterion
title_full_unstemmed Relative growth rate optimization under behavioral criterion
title_sort relative growth rate optimization under behavioral criterion
publishDate 2024
url https://hdl.handle.net/10356/173743
_version_ 1794549327649046528