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

Abstract

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 classic procedure is "myopic" with regard to potential changes in the future behavior of the agent due to inherent random fluctuations of the system. The agent's attitude to risk is rigid. Although often criticized, the most widely used hypothesis for the analysis of economic behavior is risk-neutrality. This borderline case must be envisaged with prudence in a dynamic stochastic context. The traditional measures of risk-aversion are generally too weak for making comparisons between risky situations, given the dynamic complexity of the environment. This can be highlighted in concrete problems in finance and insurance, context for which the Arrow-Pratt measures (in the small) give ambiguous results (see Ross, 1981).