Abstract: In this paper we study a new class of recursive utilities in dynamic choice processes in a stochastic environment. The basic idea is to introduce a variable measure of impatience for an economic agent. In the literature, this kind of measure is presented by a Lipschitz constant (often a contraction coefficient) concerning the aggregator. In this paper, on the other hand, the contraction property is described by some increasing real-valued function. When this function is linear, then our theory coincides with the well-known case. We make use of an extension of the Banach contraction principle given by Matkowski to derive recursive utilities and solve the associated dynamic programming problem. We present two approaches in order to take into account randomness of future outcomes. Our first approach is in spirit of the von Neumann-Morgenstern concept and is based on the notion of expectation. We construct a recursive utility on the space of trajectories of the process and then take its expected value. It turns out that the associated optimization problem leads to a non-stationary dynamic programming and an infinite system of Bellman equations, which result in obtaining persistently optimal policies. In our second approach, we construct recursive utilities on the space of policies of an agent that have a natural interpretation. The associated optimization problem leads to a solution of a single Bellman equation and deriving a stationary optimal policy for the agent. Our theory is enriched by various applications , e.g., to many growth stochastic models.
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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number
12044.
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