To formalize a nonlinear rational expectation model in macroeconomics as a functional equation, we investigate the existence of a unique solution. Assuming that the probability of large exogenous disturbance occurring is sufficiently small, we prove that a unique solution exists. This result provides a rigorous foundation for research on nonlinear rational expectation models as a natural extension of existing linear models.

中文翻译：

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下界为零的非线性有理期望方程是否存在唯一解？

为了将宏观经济学中的非线性理性预期模型形式化为函数方程，我们研究了唯一解的存在性。假设发生大的外生扰动的概率足够小，我们证明存在唯一解。这一结果为作为现有线性模型的自然延伸的非线性理性期望模型的研究提供了严格的基础。