Characterization of symmetrical monotone risk aversion in the RDEU model

In a previous paper [Cahiers de la M.S.E. (1999) 86] we proved that for RDEU (rank-dependent expected utility) maximizing MM (market-makers) with non-increasing marginal utility, positivity of the bid-ask spread can be identified with a very weak form of risk aversion SMRA (symmetrical monotone risk aversion). We perform here a more thorough study of SMRA, firstly in a general setting, and secondly in connection with the general RDEU model. Concerning the first point, SMRA is shown to be characterized via simple symmetric monotone spreads. As for the second issue, we characterize SMRA for the general RDEU model through a comparison of an index of pessimism (linked to the probability transformation function f) with an index of greediness (linked to the utility function u) in a similar way as done earlier for monotone risk aversion [Cahiers d'Ecomath (1997) 53]. (C) 2002 Elsevier Science B.V. All rights reserved.