Optimal Payoffs under Smooth Ambiguity

Abstract

We study optimal payoff choice for an investor in a one-period model under smooth ambiguity preferences, also called KMM preferences as they were 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 stock price. Our contribution is threefold. 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, in a setting of a log-normal market asset under drift and volatility uncertainty, we reveal that ambiguity leads to optimal payoffs that are no longer necessarily long in the market asset.

Keywords: Finance, model ambiguity, KMM preferences, ambiguity aversion, drift and volatility uncertainty