$L_p$中递归效用模型的存在唯一性
Existence and Uniqueness of Recursive Utility Models in $L_p$
摘要：
Epstein和Zin（1989）提出的递归偏好在现代宏观经济学和资产定价理论中扮演着不可或缺的角色。不幸的是，建立递归效用模型解的唯一存在性是不平凡的。我们证明了最严格的已知存在性和唯一性条件可以扩展到（i）Schorfheide，Song和Yaron（2018）递归效用和（ii）具有“窄框架”的递归效用。此外，我们将Borovicka和Stachurski（2019）的解空间从$L_1$锐化为$L_p$，以便结果适用于更广泛的现代资产定价模型。例如，使用$L_2$希尔伯特空间理论，我们找到了生成Bansal和Yaron（2004）以及Schorfheide，Song和Yaron（2018）模型的唯一$L_2$解的参数类。
英文摘要：
Recursive preferences, of the sort developed by Epstein and Zin (1989), play an integral role in modern macroeconomics and asset pricing theory. Unfortunately, it is non-trivial to establish the unique existence of a solution to recursive utility models. We show that the tightest known existence and uniqueness conditions can be extended to (i) Schorfheide, Song and Yaron (2018) recursive utilities and (ii) recursive utilities with `narrow framing'. Further, we sharpen the solution space of Borovicka and Stachurski (2019) from $L_1$ to $L_p$ so that the results apply to a broader class of modern asset pricing models. For example, using $L_2$ Hilbert space theory, we find the class of parameters which generate a unique $L_2$ solution to the Bansal and Yaron (2004) and Schorfheide, Song and Yaron (2018) models.
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