Improving the Risk Concept: A Revision of Arrow-Pratt Theory in the Context of Controlled Dynamic Stochastic Environments

In the literature on risk, one generally assume that uncertainty is uniformly distributed over the entire working horizon, when the absolute risk-aversion index is negative and constant. From this perspective, the risk is totally exogenous, and thus independent of endogenous risks. The traditional measures of risk-aversion are generally too weak for making comparisons between risky situations. This can be highlighted in concrete problems in finance and insurance, context for which the Arrow-Pratt measures of risk-aversion give ambiguous results (Ross 1981). We improve the Arrow-Pratt approach (1964, 1971a, 1971b), which takes into account only attitudes towards small exogenous risks, by integrating in the analysis potentially high endogenous risks that are under the control of the agent. Based on multiple theoretical and empirical arguments, this new approach offers an elegant study of the close relationship between behavior, attitude and perceived risk.