There is now a considerable amount of research on the deficiencies of additively separable preferences for effective modelling of economically meaningful behaviour. Through analysis of observational data and the design of suitable experiments, economists have constructed progressively more realistic representations of agents and their choices. For intertemporal decisions, this typically involves a departure from the additively separable benchmark. A familiar example is the recursive preference framework of Epstein and Zin (1989), which has become central to the quantitative asset pricing literature, while also finding widespread use in applications range from optimal taxation to fiscal policy and business cycles.
This thesis presents three essays which examine mathematical research questions within the context of recursive preferences and dynamic programming. The focus is particularly on showing existence and uniqueness of recursive utility processes under stationary and non-stationary consumption growth specifications, and on solving the closely related problem of optimality of dynamic programs with recursive preferences.
On one hand, the thesis has been motivated by the availability of new and unexploited techniques for studying the aforementioned questions. The techniques in question primarily build upon an alternative version of the theory of monotone concave operators proposed by Du (1989, 1990). They are typically well suited to analysis of dynamic optimality with a variety of recursive preference specifications.
On the other hand, motivation also comes from the demand side: while many useful results for dynamic programming within the context of recursive preferences have been obtained by existing literature, suitable results are still lacking for some of the most popular specifications for applied work, such as common parameterizations of the Epstein-Zin specification, or preference specifications that incorporate loss aversion and narrow framing into the Epstein-Zin framework, or the ambiguity sensitive preference specifications. In this connection, the thesis has sought to provide a new approach to dynamic optimality suitable for recursive preference specifications commonly used in modern economic analysis.
The approach to examining the problems of dynamic programming exploits the theory of monotone convex operators, which, while less familiar than that of monotone concave operators, turns out to be well suited to dynamic maximization. The intuition is that convexity is preserved under maximization, while concavity is not. Meanwhile, concavity pairs well with minimization problems, since minimization preserves concavity. By applying this idea, a parallel theory for these two cases is established and it provides sufficient conditions that are easy to verify in applications
