Production and Hedging under Smooth Ambiguity Preferences

Abstract

This paper examines the optimal production and hedging decisions of the competitive firm facing ambiguous price and background risk. Ambiguity is modeled by a second-order probability distribution that captures the firm's uncertainty about which of the subjective beliefs govern the price and background risk. Ambiguity preferences are modeled by the (second-order) expectation of a concave transformation of the (first-order) expected utility of profit conditional on each plausible subjective joint distribution of the price and background risk. When the background risk is additive in nature, we show that the separation theorem holds in that the firm's optimal production decision depends neither on the firm's attitude towards ambiguity nor on the incident of the underlying ambiguity. We derive necessary and sufficient conditions under which the firm's optimal forward position is completely characterized. When the background risk is multiplicative in nature, we derive sufficient conditions under which the firm reduces its optimal output level and opts for an under-hedge. Contrary to the conventional wisdom, we show that the behavior of the firm is affected by the introduction of ambiguity even when the firm is ambiguity neutral.