We study optimal payoff choice for an investor in a one-period model under smooth ambiguity preferences, also called KMM preferences as proposed by Klibanoff et al. (2005). In contrast to the existing literature on optimal asset allocation for a KMM investor in a one-period model, we also allow payoffs that are non-linear in the market asset. Our contribution is fourfold. First, we characterize and derive the optimal payoff under KMM preferences. Second, we demonstrate that a KMM investor solves an equivalent problem to an investor under classical subjective expected utility (CSEU) with adjusted second-order probabilities. Third, we show that a KMM investor with exponential ambiguity attitude implicitly maximizes CSEU utility under the ‘worst-case’ second-order probabilities determined by his ambiguity aversion. Fourth, we reveal that optimal payoffs under ambiguity are not necessarily monotonically increasing in the market asset, which we illustrate using a log-normal market asset under drift and volatility uncertainty.

中文翻译：

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平滑模糊下的最优收益


我们研究了平滑模糊偏好下的单期模型中投资者的最优收益选择，也称为 Klibanoff 等人（2005 年）提出的 KMM 偏好。与现有关于单期模型中 KMM 投资者最佳资产配置的文献相比，我们还允许市场资产中的非线性收益。我们的贡献有四个方面。首先，我们描述并推导出 KMM 偏好下的最佳收益。其次，我们证明 KMM 投资者在经典主观预期效用 （CSEU） 下解决了与投资者等效的问题，并调整了二阶概率。第三，我们表明，具有指数模糊态度的 KMM 投资者在由其模糊厌恶决定的“最坏情况”二阶概率下隐含地最大化了 CSEU 效用。第四，我们揭示了模糊性下的最佳收益在市场资产中不一定是单调增加的，我们使用漂移和波动性不确定性下的对数正态市场资产来说明这一点。