Arrow, Kenneth

AbstractThis article summarizes the theory of markets under uncertainty, developed by Arrow and Debreu. It describes the achievements of the theory, the critical issues that it raises, and its large legacy. This article also 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. In terms of Arrow's legacy, it is now known that 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. Kenneth Arrow encouraged the creation of a more recent extension of classic axiomatic theory of choice under uncertainty, and, in the early 1990s, we proposed axioms that treat symmetrically frequent and rare events, leading to a new definition of rationality and of choices under uncertainty that conform better to the experimental evidence. The introduction of markets with “endogenous uncertainty” in the early 1990s extended and challenged the foundation of the Arrow–Debreu theory of markets by considering risks that are created by the workings of the economy, resulting in the breakdown of the equivalence between markets with and without uncertainty that prevails in the Arrow–Debreu theory. This led to a new world of uncertainty creation through financial innovation and regulation that is at the heart of the financial markets turmoil of 2008–2009. In 1999, Arrow himself contributed to the theory of endogenous uncertainty in his work with Frank Hahn.