Xue Dong HeRoy KouwenbergXun Yu ZhouColumbia University in the City of New YorkErasmus School of EconomicsMahidol UniversityChinese University of Hong Kong2019-08-232019-08-232018-01-01Mathematical Control and Related Fields. Vol.8, No.3-4 (2018), 679-70621568499215684722-s2.0-85056544128https://repository.li.mahidol.ac.th/handle/20.500.14594/46112© 2018, American Institute of Mathematical Sciences. All rights reserved. In this paper we analyze how changes in inverse S-shaped probability weighting influence optimal portfolio choice in a rank-dependent utility model. We derive sufficient conditions for the existence of an optimal solution of the investment problem, and then define the notion of a more inverse S-shaped probability weighting function. We show that an increase in inverse S-shaped weighting typically leads to a lower allocation to the risky asset, regardless of whether the return distribution is skewed left or right, as long as it offers a non-negligible risk premium. Only for lottery stocks with poor expected returns and extremely positive skewness does an increase in inverse S-shaped probability weighting lead to larger portfolio allocations.Mahidol UniversityMathematicsArticleSCOPUS10.2139/ssrn.3067189