On recursive utilities with non-affine aggregator and conditional certainty equivalent

Abstract

In this paper, we consider the problem of the existence and the uniqueness of a recursive utility function defined on intertemporal lotteries. The purpose of this paper is to provide the results of the existence and the uniqueness of a recursive utility function. The utility function is obtained as the limit of iterations on a nonlinear operator and is independent on initial starting points, with iterations converging at an exponential rate. We also find the maximum utility and an optimal strategy by means of iterations of the Bellman operator. Keywords Recursive utilities • Dynamic programming • Epstein-Zin preferences • Certainty equivalent • Solid cone • Attracting property JEL Classification E21 • C61 • C02 • C65 • D64

Time-consistent equilibria in dynamic models with recursive payoffs and behavioral discounting

“…Also, an important technical aspect of our approach is, we introduce a new functional equation method that robustly links recursive utility models with strategic aspects of limited commitment. Our approach substantially extends and integrates separate ideas developed in a series of contributions by Balbus et al (2015bBalbus et al ( , 2018, Balbus et al (2020) and Balbus (2020), among others. In doing so, we provide the first attempt of which we are aware to analyze existence of minimal state Markovian equilibrium in dynamic economies with general recursive payoffs and time-inconsistent preferences.…”

“…17 For more recent recursive preferences literature, the reader is referred to works by Le Van and Vailakis (2005), Rincon-Zapatero and Rodriguez-Palmero (2009), Martins-da Rocha and Vailakis (2010), Matkowski and Nowak (2011), Galperti and Strulovici (2017), Bich et al (2018) and Balbus (2020).…”

Time Consistent Equilibria in Dynamic Models With Recursive Payoffs and Behavioral Discounting

“…Also, an important technical aspect of our approach is, we introduce a new functional equation method that robustly links recursive utility models with strategic aspects of limited commitment. Our approach substantially extends and integrates separate ideas developed in a series of contributions by Balbus et al (2015bBalbus et al ( , 2018, Balbus et al (2020) and Balbus (2020), among others. In doing so, we provide the first attempt of which we are aware to analyze existence of minimal state Markovian equilibrium in dynamic economies with general recursive payoffs and time-inconsistent preferences.…”

Do not Blame Bellman: It Is Koopmans' Fault

“…This property is shared by a large class of aggregators commonly used in applications, beginning with Epstein–Zin preferences. Dynamic programming with a value‐concave aggregator was studied by Balbus (2020), Bloise and Vailakis (2018), and Ren and Stachurski (2021). This promising approach is frustrated by the fact that uniqueness only obtains in the interior of the domain, or subject to some appropriate boundary condition.…”