On History-Dependent Optimization Models : A Unified Framework to Analyze Models with Habits, Satiation and Optimal Growth

In this paper, we first provide a framework for history-dependent utility models. We further consider discrete infinite horizon dynamic optimization programs in which the instantaneous payoff presents such historydependence. Habits are a particular case of history-dependence. An issue about models with habits is their lack of general framework. Our framework allows to study habit models that are either additive or multiplicative or neither, as well as satiation models. Moreover, with this unified setting one can treat the usual optimal growth models with or without habit formation and with or without satiation effects. As the way the history dependence is formalized allows us to use dynamic programming tools. We show that the value function is the unique fixed point of the Bellman operator. Such history-dependent modelizations have their motivations and applications in many areas among which decision theory, psychology, behavioral and environmental economics