Distorted probabilities and choice under risk (Q1202128)

The monograph reviews the existing axiomatic utility theories, such as the classical von Neumann-Morgenstern theory and its modifications. Quiggin's anticipated utility theory or Yaari's dual theory and presents some new facts concerning general rank-dependent utility theory in which a utility \(v(x,p)\) is orginally ascribed to elementary lotteries (i.e. ones giving a win of \(x\) with probability \(p\) and status quo with probability \(1-p\)) and then extended to arbitrary distributions. These results extend those due to Green and Jullien. Especially analyzed is the case where \(v(x,p)\) has the form \(u(x)p^{g(x)}\), in particular, the author offers then an explanation of the Allais paradox. In a separate chapter, the author considers the problem of risk aversion in this framework and discusses relations to earlier models due to Arrow and Pratt or Friedman and Savage.