Abstract

Models of precautionary saving or storage include cases where the marginal value of accumulated balances is unbounded, with an invariant distribution with infinite mean. Based on a uniform continuity argument, we show that a model of saving with bounded marginal value can be used to approximate the unbounded marginal value function, and the quantiles of its invariant distribution, arbitrarily accurately. These results offer a foundation for a strategy for numerical solution of marginal values in cases where they are unbounded, and for derivation of the quantiles of their invariant distributions. © 2007 Elsevier B.V. All rights reserved.