Asymptotic Growth under Uncertainty: Existence and Uniqueness
This paper demonstrates, using the Reflection Pri nciple, the existence and uniqueness of the solution to the classic Solow equati on under continuous time uncertainty for the class of strictly concave productio n functions which are continuously differentiable on the nonnegative real number s. This class contains all CES functions with elasticity of substitution less th an unity. A steady-state distribution also exists for this class of production f unctions which have a bounded slope at the origin. A condition on thedrift-vari ance ratio of the stochastic differential equation alone is found to be necessar y for the existence of a steady state. Copyright 1987 by The Review of Economic Studies Limited.
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Volume (Year): 54 (1987)
Issue (Month): 1 (January)
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