MIXTURE OF CONSISTENT STOCHASTIC UTILITIES AND A PRIORI RANDOMNESS

Abstract

The purpose of this paper is to develop an explicit construction of consistent utilities, using the stochastic flows approach developed in El Karoui & Mrad (2013, 2020). Starting from a family of utility functions indexed by some parameter [Formula: see text] (for example, the risk aversion coefficient or any other parameter), the idea is to randomize [Formula: see text] and to construct nonstandard stochastic utility processes. Two approaches are developed. The first one consists of building directly from the class [Formula: see text] a global utility [Formula: see text] as a sup-convolution. The second approach which is very different, consists to define from the class [Formula: see text] of monotonic optimal processes, associated with the class [Formula: see text], a global pair [Formula: see text] as a mixture. The nonstandard stochastic utility is then obtained by composing stochastic flows and is interpreted as the aggregate utility of all considered agents.