Optimal Investment with Noise Trading Risk

This paper investigates the optimal dynamic investment for an investor who maximizes constant absolute risk aversion (CARA) utility in a discrete-time market with a riskfree bond and a risky stock. The risky stock is assumed to present both the dividend risk and the price risk. With our assumptions, the dividend risk is equivalent to fundamental risk, and the price risk is equivalent to the noise trading risk. The analytical expression for the optimal investment strategy is obtained by dynamic programming. The main result in this paper highlights the importance of differentiating between noise trading risk and fundamental risk for the optimal dynamic investment. Xu acknowledges the Institute for Quantitative Finance and Insurance (IQFI) at the University of Waterloo. Li would like to acknowledge the National Science Foundation of China under Grant No. 70518001, the National Basic Research Program of China (973 Program) under Grant No. 2007CB814902, and the Social Science & Humanities foundation of Ministry of Education of China under Grant No. 07JA630031. Tan acknowledges the funding from the Canada Research Chairs Program, the Natural Sciences and Engineering Research Council of Canada, and the Cheung Kong Scholar Program of China.