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...
| Main Authors: | , , |
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| מחברים אחרים: | |
| פורמט: | Journal Article |
| שפה: | English |
| יצא לאור: |
2024
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| נושאים: | |
| גישה מקוונת: | https://hdl.handle.net/10356/173743 |
| _version_ | 1826115004534882304 |
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| author | Peng, Jing Wei, Pengyu Xu, Zuo Quan |
| author2 | Nanyang Business School |
| author_facet | Nanyang Business School Peng, Jing Wei, Pengyu Xu, Zuo Quan |
| author_sort | Peng, Jing |
| collection | NTU |
| 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. |
| first_indexed | 2024-10-01T03:48:27Z |
| format | Journal Article |
| id | ntu-10356/173743 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T03:48:27Z |
| publishDate | 2024 |
| record_format | dspace |
| spelling | ntu-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. |
| spellingShingle | Business and Management Behavioral finance Prospect theory Peng, Jing Wei, Pengyu Xu, Zuo Quan Relative growth rate optimization under behavioral criterion |
| title | 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_short | Relative growth rate optimization under behavioral criterion |
| title_sort | relative growth rate optimization under behavioral criterion |
| topic | Business and Management Behavioral finance Prospect theory |
| url | https://hdl.handle.net/10356/173743 |
| work_keys_str_mv | AT pengjing relativegrowthrateoptimizationunderbehavioralcriterion AT weipengyu relativegrowthrateoptimizationunderbehavioralcriterion AT xuzuoquan relativegrowthrateoptimizationunderbehavioralcriterion |