Anything is Possible: On the Existence and Uniqueness of Equilibria in the Shleifer-Vishny Model of Limits of Arbitrage

This paper characterizes equilibria in the Shleifer-Vishny model of limits of arbitrage. To prove existence, one has to consider types of equilibria ignored by Shleifer and Vishny, even if one adopts their parameter restrictions. For example, the only equilibrium may be one in which maximization of expected wealth requires an “all-or-nothing” investment strategy, with intermediate investment levels being strictly unprofitable. If one goes beyond Shleifer and Vishny's parameter restrictions, multiple equilibria may arise, and equilibrium selection may be governed by sunspots. Moreover, there...

This paper characterizes equilibria in the Shleifer-Vishny model of limits of arbitrage. To prove existence, one has to consider types of equilibria ignored by Shleifer and Vishny, even if one adopts their parameter restrictions. For example, the only equilibrium may be one in which maximization of expected wealth requires an “all-or-nothing” investment strategy, with intermediate investment levels being strictly unprofitable. If one goes beyond Shleifer and Vishny's parameter restrictions, multiple equilibria may arise, and equilibrium selection may be governed by sunspots. Moreover, there may exist an equilibrium in which the asset price returns to fundamentals despite worsening noise trader sentiment.