This note studies conditions under which sequences of state variables generated by discrete-time stochastic optimal accumulation models have law of large numbers and central limit properties. Productivity shocks with unbounded support are considered. Instead of restrictions on the support of the...

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...

Ekeland and Scheinkman (1986) prove the necessity of a standard transversality condition under certain technical conditions. Their result is one of the most powerful on the necessity of a transversality condition currently available in the literature, and their proof involves numerous...

This note provides a simple proof of the necessity of the transversality condition for the differentiable reduced-form model. The proof uses only an elementary perturbation argument without relying on dynamic programming. The proof makes it clear that, contrary to common belief, the necessity of...

We study a simple infinite horizon model with indivisible labor. We characterize the optimal plans under the assumptions that $\beta R = 1$ and that $1/2 \leq \beta 1$, where R is the gross interest rate and $\beta$ is the discount factor. We show that under those assumptions, optimal plans are...

This paper studies conditions under which the price of an asset is uniquely determined by its fundamental value - i.e., no bubbles can arise - in Lucas-type asset pricing models with unbounded utility. After discussing Gilles and LeRoy's (1992) example, we construct an example of a two-period,...