Risk Aversion for Investors with Memory: Hereditary Generalizations of Arrow-Pratt Measure

The paper proposes a generalization of the Arrow-Pratt measures of absolute risk-aversion (ARA) for the case of financial processes with memory. The authors take into account the presence of the investors’memory in the description of their behavior. Standard risk aversion measures, which are defined by derivatives of integer orders, are actually based on the assumption of investors’ amnesia, because these derivatives are determined by the properties of the function only in an infinitesimal neighborhood of the point (point in time or amount of wealth). The authors propose a method that allows them to refuse the assumptions about absence of a memory about changes of the utility function and value of assets. In order to take into account the memory effects the authors used mathematical tools of derivatives (integro-differentiations) of non-integer orders. Formulas of hereditary generalizations.