Solving heterogeneous-belief asset pricing models with short-selling constraints and many agents

Short-selling constraints are common in financial markets, while physical assets such as housing often lack markets for short-selling altogether. As a result, investment decisions are often restricted by such constraints. This paper studies asset prices in behavioral heterogeneous-belief models with short-selling constraints and arbitrarily many belief types. We provide conditions on beliefs such that short-selling constraints bind for different types, along with analytic expressions for price and demands that allow us to construct fast solution algorithms relevant for a wide range of models. An application studies how an alternative uptick rule, as in the United States, affects price dynamics and wealth distribution in a market with many belief types in evolutionary competition. In a numerical example, we highlight a scenario in which a modified version of the alternative uptick rule, triggered by smaller percentage falls in price, reduces both asset mispricing and wealth inequality relative to the current regulation. As extensions, we show how our method applies to multiple asset markets with short-selling constraints, additional heterogeneities, and price setting by a market maker.