Optimal Payoffs under Smooth Ambiguity

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, P., Marinacci, M., & Mukerji, S. (2005). A smooth model of decision making under ambiguity. Econometrica, 73 (6), 1849–1892). 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.