This paper shows stochastic versions of (i) Michel's (1990, Econometrica 58, 705--723, Theorem 1) necessity result , (ii) a generalization of the TVC results of Weitzman (1973, Manage. Sci. 19, 783--789) and Ekeland and Scheinkman (1986, Math. Oper. Res. 11, 216--229), and (iii) Kamihigashi's...

Production takes time, and labor supply and profit maximization decisions that relate to current production are typically made before all shocks affecting that production have been realized. In this paper we re-examine the problem of stochastic optimal growth with aggregate risk where the timing...

In equilibrium models of firm dynamics, the stationary equilibrium distribution of firms summarizes the predictions of the model for a given set of primitives. Focusing on Hopenhayn's seminal model of firm dynamics with entry and exit (Econometrica, 60:5, 1992, p.~1127--1150), we provide an...

In this paper, we give Necessary and Sufficient Conditions for a Solution of the Belman Equation to be the Value Function. This result is a general principle. It requires no structure beyond the common framework of discrete-time stationary optimization problems with time-additive returns. In...

In equilibrium models of firm dynamics, the stationary equilibrium distribution of firms summarizes the predictions of the model for a given set of primitives. Focusing on Hopenhayn's seminal model of firm dynamics with entry and exit (Econometrica, 60:5, 1992, p. 1127–1150), we provide an...

In this paper we show that multiple interior steady states are possible in the Ramsey model with elastic labor supply. In particular we establish the following three results: (i) for any discount factor and production function, there is a utility function such that a continuum of interior steady...

In this note, we discuss an order-theoretic approach to dynamic programming. In particular, we explain how order-theoretic fixed point theorems can be used to establish the existence of a fixed point of the Bellman operator, as well as why they are not sufficient to characterize the value...

We establish some elementary results on solutions to the Bellman equation without introducing any topological assumption. Under a small number of conditions, we show that the Bellman equation has a unique solution in a certain set, that this solution is the value function, and that the value...

We establish some elementary results on solutions to the Bellman equation without introducing any topological assumption. Under a small number of conditions, we show that the Bellman equation has a unique solution in a certain set, that this solution is the value function, and that the value...

In this note, we show that the least xed point of the Bellman op- erator in a certain set can be computed by value iteration whether or not the xed point is the value function. As an application, we show one of the main results of Kamihigashi (2014a) with a simpler proof.