Rank-dependent utility and risk taking in complete markets

Abstract

© 2017 Society for Industrial and Applied Mathematics. Experimental studies show that people's risk preferences depend nonlinearly on probabilities, but relatively little is known about how probability weighting inuences investment decisions. In this paper we analyze the portfolio choice problem of investors who maximize rank-dependent utility in a single-period complete market. We prove that investors with a less risk averse preference relation in general choose a more risky final wealth distribution, receiving a risk premium in return for accepting conditional-mean-zero noise (more risk). We also propose a new scenario-based notion of less risk taking that can be applied when state probabilities are unknown or not agreed upon.