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...

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...

The stochastic dominance ordering over probability distributions is one of the most familiar concepts in economic and financial analysis. One difficulty with stochastic dominance is that many distributions are not ranked at all, even when arbitrarily close to other distributions that are....

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...

The stochastic dominance ordering over probability distributions is one of the most familiar concepts in economic and financial analysis. One difficulty with stochastic dominance is that many distributions are not ranked at all, even when arbitrarily close to other distributions that are....

We show that the critical capital stock of the Dechert and Nishimura (1983) model is a decreasing and continuous function of the discount factor. We also show that the critical capital stock merges with a nonzero steady state as the discount factor decreases to a certain boundary value, and that...

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...

Random dynamical systems encountered in economics have certain distinctive characteristics that make them particularly well suited to analysis using the tools for studying Markov processes developed by Rabi N. Bhattacharya and his coauthors over the last few decades. In this essay we discuss the...

In this note, we show that the least fixed point of the Bellman operator in a certain set can be computed by value iteration whether or not the fixed point is the value function. As an application, we show one of the main results of Kamihigashi (2014, "Elementary results on solutions to the...

We consider infinite-horizon deterministic dynamic programming problems in discrete time. We show that the value function is always a fixed point of a modified version of the Bellman operator. We also show that value iteration monotonically converges to the value function if the initial function...