Mixture of consistent stochastic utilities, and a priori randomness

The purpose of this paper is to develop an explicit construction of consistent utilities, using the stochastic flows approach developed in [KM13] and [KM16]. Starting from a family of utility functions indexed by some parameter α (for example the risk aversion of different agents), the idea is to randomize α and construct a non standard stochastic utilities processes. Two approach are developed, the first one consists to built directly from the class {U α , α ∈ R} a global one U as a sup-convolution. The second approach which is very different, consists to define from a class (X α , Y α) α∈R of monotonic processes a global pair (X * , Y *) as a mixture. The non standard stochastic utility is then obtained by composing stochastic flows and interpreted as the aggregate utility of all considered agents .