Asset Pricing with Short-Selling Constraints and Many Belief Types: Three Fast Solution Algorithms

Short-selling is common in financial markets but is also strictly regulated. When short selling is banned, heterogeneous beliefs determine which investors take long positions and which have constrained positions of zero in equilibrium. Solving such models is computationally intensive. We set out three algorithms suited to solving models with very large numbers of investor types – such as millions – quickly on a standard laptop or desktop computer. The fastest algorithm combines price iterations with a divide and conquer approach. As an application we study the impact of a short-selling ban on price dynamics and wealth distribution in a market of many investor types in evolutionary competition, and we observe that both can be affected substantially.