Asymptotic Growth under Uncertainty: Existence and Uniqueness
Asymptotic Growth under Uncertainty: Existence and Uniqueness
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不确定性下的渐近增长：存在性与唯一性
DOI：
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发表时间：
1987
期刊：
影响因子：
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通讯作者：
A. Malliaris
中科院分区：
文献类型：
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作者：
F. Chang;A. Malliaris
本文利用反射原理证明了非负实数上连续可导的一类严格凹生产函数在连续时间不确定性下经典索洛方程解的存在性和唯一性。此类包含所有替代弹性小于 1 的 CES 函数。此类生产函数也存在稳态分布，其在原点处具有有界斜率。人们发现，独立于技术和储蓄率的随机微分方程的漂移-方差比条件对于稳定状态的存在是必要的。
This paper demonstrates, using the Reflection Principle, the existence and uniqueness of the solution to the classic Solow equation under continuous time uncertainty for the class of strictly concave production functions which are continuously differentiable on the nonnegative real numbers. This class contains all CES functions with elasticity of substitution less than unity. A steady state distribution also exists for this class of production functions which have a bounded slope at the origin. A condition on the drift-variance ratio of the stochastic differential equation alone, independent of technology and the savings ratio, is found to be necessary for the existence of a steady state.