Rank-Dependent Utility and Risk Taking in Complete Markets

We analyze the portfolio choice problem of investors who maximize rankdependent utility in a single-period complete market. We propose a new notion of less risk taking: choosing optimal terminal wealth that pays off more in bad states and less in good states of the economy. We prove that investors with a less risk averse preference relation in general choose more risky terminal wealth, receiving a risk premium in return for accepting conditional-zero-mean We thank Shigeo Kusuoka, Christoph Kuzmics, Peter Wakker, seminar participants at Oxford, as well as conference participants at the 2014 Econometric Society European Meeting in Toulouse, the 2014 INFORMS Annual Meeting in San Francisco, the 2014 SIAM Conference on Financial Mathematics and Engineering in Chicago, the Fourth IMS Finance, Probability and Statistics Workshop in Sydney, the Seventh International Symposium on Backward Stochastic Differential Equations in Weihai, the 2014 International Conference on Portfolio Selection and Asset Pricing in Kyoto, the 2014 CUHK Symposium in Financial Risk Management in Hong Kong, the 2014 Big Data and Quantitative Behavioral Finance Conference in Nanjing. He acknowledges financial support from a start-up fund at Columbia University. Zhou acknowledges financial support from a start-up fund at the University of Oxford, a research fund from the Oxford-Man Institute of Quantitative Finance, and a research fund from East China Normal University. Corresponding Author. Department of Industrial Engineering and Operations Research, Columbia University, Room 315, Mudd Building, 500 W. 120th Street, New York, NY 10027, US. Email: [email protected]. Telephone: +1-212-854-2936. Mahidol University, College of Management, Bangkok, Thailand; Erasmus University Rotterdam, Erasmus School of Economics, Rotterdam, The Netherlands; Email: [email protected]. Mathematical Institute, The University of Oxford, Woodstock Road, OX2 6GG Oxford, UK, and Oxford–Man Institute of Quantitative Finance, The University of Oxford; Email: [email protected].