Neural Networks for Non-independent Lotteries

Abstract

The von Neuman-Morgenstern utility functions play a relevant role in the set of utility functions. This paper shows the density of the set von Neuman- Morgenstern utility functions on the set of utility utility function that can represent arbitrarily well a given continuous but not independent preference relation over monetary lotteries. The main result is that without independence it is possible to approximate utility functions over monetary lotteries by von Neuman-Morgenstern ones with arbitrary precision. The approach used is a constructive one. Neural networks are used for their approximation properties in order to get the result, and their functional form provides both the von Neumann-Morgenstern representation and the necessary change of variables over the set of lotteries.