The Generalized Arrow-Pratt Coefficient

A vector-valued generalized Arrow-Pratt (GAP) coefficients is defined for a utility defined on a Hilbert outcome space. Given risk averse, increasing and twice differentiable utilities on such outcome spaces, comparisons of their risk aversion using GAP coefficients are congruent to comparisons using well-founded decision-theoretic criteria. The Hilbert space setting admits risks embodied in a significant class of random processes, especially second-order processes. We also provide a theoretically well-founded and computationally tractable method for estimating the realized GAP coefficient from observed data when the outcome space is a reproducing kernel Hilbert space