General Equilibrium with Uncertainty: The Work of Kenneth Arrow

This article summarizes the theory of markets under uncertainty that Arrow and Debreu created, its achievements and the critical issues that it raises. It focuses on the way Arrow introduced securities: how he defined them and what were the most useful developments of this theory. It mentions the theory of insurance that Arrow pioneered together with Malinvaud and others, and Arrow’s theory of risk bearing that follows the axiomatic treatment of Von Neumann and Morgenstern, Milnor, Hernstein, De Groot, and Villegas. The classic expected utility theory embraces normal or frequent risks at the expense of neglecting rare events, even those with important consequences such as catastrophes, causing paradoxical experimental behavior as shown by the author. Kenneth Arrow encouraged the creation of an extension of classic axiomatic theory, and in the early 1990s the author proposed axioms that treat symmetrically frequent and rare events, leading to a new definition of rationality and a new form of choice under uncertainty that conforms better to the experimental evidence. Additionally, the introduction of markets with endogenous uncertainty in the early 1990s challenged the foundation of Arrow Debreu's theory of markets. Endogenous uncertainty is generated by the workings of the economy, and breaks down the equivalence between markets with and without uncertainty that prevails in Arrow Debreu's theory. This leads to a new world of uncertainty creation through financial innovation and regulation that is at the heart of the financial markets turmoil of 2008. In 1999 Arrow contributed to the theory of endogenous uncertainty in his work with Frank Hahn.