Constant Exchange Risk Properties

This paper develops a methodology using risk properties to characterize the functional form of a utility measure for decision making under uncertainty. The constant absolute risk property, for example, is known to be necessary and sufficient, with appropriate regularity conditions, for the utility function to have either a linear or an exponential form. A new generalization of this property, called the constant exchange risk property, gives a characterization of six utility functions: the linear function, the exponential function, the quadratic function, the sum of two exponential functions, the sum of a linear and an exponential function, and the product of a linear and an exponential function. Since all of these functional forms have been used previously as approximations, this methodology allows analysts to distinguish beforehand between alternative forms and thus properly specify the utility function in applications.