Probability weighting functions and heavy tailed returns

• Probability weighting transforms finite-variance distributions into heavy-tailed stable ones. • A rescaled Normal characteristic function becomes a Cauchy distribution under this weighting. • Modified binomial models converge to symmetric stable distributions. • The framework links behavioral biases with misperceived market risks. Heavy tailed distributions are characteristic of financial returns. Building on behavioral economic models and, in particular, on Dombi’s modifier operator, we show that applying probability weighting on symmetric distributions with finite moments transforms them into heavy-tailed stable distributions. Our approach highlights that when the generator is chosen as f ( x ) = − ln x , the Dombi modifier operator exactly reproduces Prelec’s function-and, as demonstrated in Dombi and Jónás (2020), Prelec’s function also arises as the limit of the epsilon weighting function. These findings provide microfoundations linking behavioral probability distortions with observed return distributions.