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The Generalized Arrow-Pratt Coefficient

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  • Sudhir A. Shah

    (Centre for Development Economics, Delhi School of Economics, University of Delhi, India)

Abstract

We define vector-valued generalized Arrow-Pratt (GAP) coefficients 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. We use the GAP coefficients to predict the effect of differences in risk aversion on an asset portfolio when assets are specified by dividend processes. Finally, we show a duality between utility functions on Euclidean spaces and GAP coeficients.

Suggested Citation

  • Sudhir A. Shah, 2016. "The Generalized Arrow-Pratt Coefficient," Working papers 254, Centre for Development Economics, Delhi School of Economics.
    • Handle: RePEc:cde:cdewps:254
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