Psychophysical laws in risk theory

Abstract

In this article specific hypotheses on the shape of a rational agent's risk preference function are derived from psychophysical laws. Weber's law is used to establish the hypothesis of constant relative risk aversion for a myopic expected-utility maximizer. Weber's law. Fechner's law and a modified version of Koopmans' preference functional are shown to generate a family of multiperiod preference functionals which are either of an additive logarithmic or a multiplicative Cobb-DougIas type. This family has very appealing implications in a world of stochastic constant returns to scale. For the actual decision the multiperiod optimizer exhibits constant relative risk aversion as does the myopic optimizer. However, with the passage of time. the degree of this risk aversion, in general, moves towards unity. Moreover, it is worth noting that the agent neither has to make the consumption decision simultaneously with the selection of an optimal risk project nor needs any information about the future except his or her own preferences.