COMPARATIVE DYNAMICS IN STOCHASTIC MODELS WITH RESPECT TO THE L∞–L∞ DUALITY: A DIFFERENTIAL APPROACH

Kenji Sato and Makoto Yano

Macroeconomic Dynamics, 2012, vol. 16, issue S1, 127-138

Abstract: Many economic analyses are based on the property that the value of a commodity vector responds continuously to a change in economic environment. As is well known, however, many infinite-dimensional models, such as an infinite–time horizon stochastic growth model, lack this property. In the present paper, we investigate a stochastic growth model in which dual vectors lie in an L∞ space. This result ensures that the value of a stock vector is jointly continuous with respect to the stock vector and its support price vector. The result is based on the differentiation method in Banach spaces that Yano [Journal of Mathematical Economics 18 (1989), 169–185] develops for stochastic growth models.

Date: 2012
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