NONPARAMETRIC NUMERICAL APPROACHES TO PROBABILITY WEIGHTING FUNCTION CONSTRUCTION FOR MANIFESTATION AND PREDICTION OF RISK PREFERENCES

Probability weighting function (PWF) is the psychological probability of a decision-maker for ob-jective probability, which reflects and predicts the risk preferences of decision-maker in behavioral decision-making. The existing approaches to PWF estimation generally include parametric methodologies to PWF con-struction and nonparametric elicitation of PWF. However, few of them explores the combination of parametric and nonparametric elicitation approaches to approximate PWF. To describe quantitatively risk preferences, the Newton interpolation, as a well-established mathematical approximation approach, is introduced to task-specifi-cally match PWF under the frameworks of prospect theory and cumulative prospect theory with descriptive psy-chological analyses. The Newton interpolation serves as a nonparametric numerical approach to the estimation of PWF by fitting experimental preference points without imposing any specific parametric form assumptions. The elaborated nonparametric PWF model varies in accordance with the number of the experimental preference points elicitation in terms of its functional form. The introduction of Newton interpolation to PWF estimation into decision-making under risk will benefit to reflect and predict the risk preferences of decision-makers both at the aggregate and individual levels. The Newton interpolation-based nonparametric PWF model exhibits an inverse S-shaped PWF and obeys the fourfold pattern of decision-makers' risk preferences as suggested by previous empirical analyses.

Automated summary

Probability weighting function (PWF) is the psychological probability of a decision-maker for objective probability, reflecting and predicting risk preferences in behavioral decision-making. The combination of parametric and nonparametric approaches to approximate PWF is rarely explored. This study introduces the Newton interpolation, a well-established mathematical approximation, to task-specifically match PWF. The nonparametric PWF model based on Newton interpolation exhibits an inverse S-shaped pattern and aligns with empirical analyses of decision-makers' risk preferences.