A class of tractable incomplete-market models for studying asset returns and risk exposure

We present a class of tractable incomplete-market models, where agents face both aggregate risk and limited participation in financial markets. Tractability relies on the assumptions of small asset volumes and of a period utility function that is linear beyond a threshold, in line with Fishburn's (1977) contribution in decision theory. We prove the existence of an equilibrium and derive theoretical results regarding asset prices and consumption choices. This small-trade model is able to reproduce a low safe return and a high equity premium, together with a realistic representation of household exposure to both idiosyncratic and aggregate risks.