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 α (for example, the risk aversion coefficient or any other parameter), the idea is to randomize α and to construct nonstandard stochastic utility processes. Two approaches are developed. The first one consists of building directly from the class {Uα,α ∈ ℝ} a global utility U as a sup-convolution. The second approach which is very different, consists to define from the class (Xα,Yα) α∈ℝ of monotonic optimal processes, associated with the class {Uα,α ∈ ℝ}, a global pair (X∗,Y∗) 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.

中文翻译：

---

一致的随机效用和先验随机性的混合

本文的目的是使用 El Karoui & Mrad (2013, 2020) 中开发的随机流方法开发一致效用的显式构造。从由某个参数索引的一系列效用函数开始α（例如，风险厌恶系数或任何其他参数），想法是随机化α并构建非标准随机效用过程。开发了两种方法。第一个包括直接从类构建{üα,α ∈ ℝ}全局实用程序ü作为上卷积。第二种方法非常不同，包括从类中定义(Xα,是α) α∈ℝ与类相关的单调最优过程{üα,α ∈ ℝ}, 一个全局对(X*,是*)作为混合物。然后通过组合随机流获得非标准随机效用，并将其解释为所有考虑的代理的总效用。