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).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 which are under the control of the agent.This point of view has strong implications on the agent's adaptive behavior towards risk in a changing environment.It can be seen as a step further in the refinement of the risk-aversion concept.It is necessary to have a very good understanding of the way the evolution of the environment affects the risk perception of rational decision-makers.Based on multiple theoretical and empirical arguments, this new approach offers an elegant study of the close relationship between behavior, attitude and perceived risk.

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