经济
数学
鞅(概率论)
终值
计量经济学
期望效用假设
文件夹
随机贴现因子
数理经济学
数学优化
资本资产定价模型
应用数学
金融经济学
微观经济学
净现值
生产(经济)
作者
Jing Peng,Pengyu Wei,Zuo Quan Xu
出处
期刊:Siam Journal on Financial Mathematics
[Society for Industrial and Applied Mathematics]
日期:2023-10-25
卷期号:14 (4): 1140-1174
摘要
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 -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.
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