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.

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Keywords Inverse S-shaped weighting function, Optimal stock holding, Portfolio selection, Probability weighting, Rank-dependent utility
JEL Portfolio Choice; Investment Decisions (jel G11)
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Journal Mathematical Control and Related Fields
He, X.D, Kouwenberg, R.R.P, & Zhou, X.Y. (2017). Inverse S-shaped probability weighting and its impact on investment. Mathematical Control and Related Fields, 8(3-4), 679–706. doi:10.2139/ssrn.3067189