An additive model of decision making under risk and ambiguity

Abstract

We extend the mean–variance (risk–value) tradeoff model to decision making under both risk and ambiguity. This model explicitly captures the tradeoff between the magnitude of risk and the magnitude of ambiguity. A measure that ranks lotteries in terms of the magnitude of ambiguity can also be obtained using this separation. By applying our model to asset pricing under ambiguity, we show that the equity premium can be decomposed into two parts: the risk premium and the ambiguity premium. Further, combining this model with the standard risk–value model, we build on the risk–ambiguity tradeoff to provide the value–risk–ambiguity preference model that does not rely on an approximation argument as the mean–variance model.