The pricing kernel under proportional ambiguity

The pricing kernel is an important tool for understanding asset prices, expected returns, and investor preferences. However, empirical findings often reveal deviations from theoretical predictions, leading to the so-called "pricing kernel puzzle". This article explores the pricing kernel under Knightian uncertainty driven by identifiable business cycles. In a pure exchange economy with a representative agent exhibiting smooth ambiguity preferences, the pricing kernel is derived from equilibrium asset prices. By linking normal variance-mean mixtures with model uncertainty, we account for agents facing uncertainty across a continuum of economic regimes. Our results show that the pricing kernel can either decrease monotonically or exhibit a U-shape, depending on the level of ambiguity aversion. Additionally, we provide economic insights into the conditions that give rise to a U-shaped pricing kernel.