Optimal payoffs under smooth ambiguity
研究了平滑模糊偏好下投资者在单期模型中的最优收益选择，允许非线性收益，发现模糊厌恶可能导致最优收益不随市场资产单调递增。
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. • We derive the optimal payoff under smooth ambiguity preferences in a static model. • We study the impact of ambiguity aversion on the optimal payoff. • The optimal payoff may not increase in the market asset. • We illustrate our results in a setting with drift and volatility uncertainty.