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.

This paper studies the global dynamics of a class of infinitely repeated two-player games in which the action space of each player is an interval, and the one-shot payoff of each player is additively separable in actions. We define an immediately reactive equilibrium (IRE) as a pure-strategy...

Transversality conditions are optimality conditions often used along with Euler equations to characterize the optimal paths of dynamic economic models. This article explains the foundations of transversality conditions using a geometric example, a finite horizon problem, and an infinite horizon...

This paper studies a one-sector stochastic optimal growth model with i.i.d. productivity shocks in which utility is allowed to be bounded or unbounded, the shocks are allowed to be bounded or unbounded, and the production function is not required to satisfy the Inada conditions at zero and...

This paper studies a one-sector optimal growth model with linear utility in which the production function is generally nonconvex, nondifferentiable, and discontinuous. The model also allows for a general form of irreversible investment. We show that every optimal path either converges to zero or...

This note studies a general nonstationary infinite-horizon optimization problem in discrete time. We allow the state space in each period to be an arbitrary set, and the return function in each period to be unbounded. We do not require discounting, and do not require the constraint...

This paper establishes (i) an extension of Michel's (1990, Theorem 1) necessity result to an abstract reduced-form model, (ii) a generalization of the results of Weitzman (1973) and Ekeland and Scheinkman (1986), and (iii) a new result that is useful particularly in the case of homogeneous...