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Certainty equivalent measures of risk

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Abstract

We study a framework for constructing coherent and convex measures of risk that is inspired by infimal convolution operator, and which is shown to constitute a new general representation of these classes of risk functions. We then discuss how this scheme may be effectively applied to obtain a class of certainty equivalent measures of risk that can directly incorporate preferences of a rational decision maker as expressed by a utility function. This approach is consequently employed to introduce a new family of measures, the log-exponential convex measures of risk. Conducted numerical experiments show that this family can be a useful tool for modeling of risk-averse preferences in decision making problems with heavy-tailed distributions of uncertain parameters.

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Acknowledgments

This work was supported in part by the Air Force Office of Scientific Research Grant FA9550-12-1-0142 and National Science Foundation Grant EPS1101284. In addition, support by the Air Force Research Laboratory Mathematical Modeling and Optimization Institute is gratefully acknowledged.

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  1. 3131 Seamans Center for the Engineering Arts and Sciences, Iowa City, IA, 52242, USA

    Alexander Vinel & Pavlo A. Krokhmal

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  1. Alexander Vinel
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  2. Pavlo A. Krokhmal
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Correspondence to Pavlo A. Krokhmal.

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Vinel, A., Krokhmal, P.A. Certainty equivalent measures of risk. Ann Oper Res 249, 75–95 (2017). https://doi.org/10.1007/s10479-015-1801-0

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