A contribution to duality theory,applied to the measurement of risk aversion

This paper determines the precise connection between the curvature properties of an objective function and the ray-curvature properties of its dual. When the objective function is interpreted as a Bernoulli or cardinal utility function, our results characterize the relationship between an agent’s attitude towards income risks and her attitude towards risks in the underlying consumption space. We obtain these results by developing and applying a number of representation theorems for concave functions.The work of Juan E. Martínez-Legaz has been supported by the Spanish Ministry of Science and Technology and the FEDER, project BEC2002-00642, and by the Departament d’Universitats, Recerca i Societat de la Informació, Direcció General de Recerca de la Generalitat de Catalunya, project 2001SGR-00162. He also thanks the Barcelona Economics Program of CREA for its support. John Quah would like to acknowledge with gratitude the financial support of the ESRC (grant number R000271171). He would also like to thank the Department of Economics at UC Berkeley, whose hospitality he enjoyed while completing this project. Both authors would like to thank Simon Cowan for pointing the way to some important references. They are also very grateful to the referee whose insightful suggestions led to a much improved paper