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Mean‐Deviation Analysis in the Theory of Choice

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  • Bogdan Grechuk
  • Anton Molyboha
  • Michael Zabarankin

Abstract

Mean‐deviation analysis, along with the existing theories of coherent risk measures and dual utility, is examined in the context of the theory of choice under uncertainty, which studies rational preference relations for random outcomes based on different sets of axioms such as transitivity, monotonicity, continuity, etc. An axiomatic foundation of the theory of coherent risk measures is obtained as a relaxation of the axioms of the dual utility theory, and a further relaxation of the axioms are shown to lead to the mean‐deviation analysis. Paradoxes arising from the sets of axioms corresponding to these theories and their possible resolutions are discussed, and application of the mean‐deviation analysis to optimal risk sharing and portfolio selection in the context of rational choice is considered.

Suggested Citation

  • Bogdan Grechuk & Anton Molyboha & Michael Zabarankin, 2012. "Mean‐Deviation Analysis in the Theory of Choice," Risk Analysis, John Wiley & Sons, vol. 32(8), pages 1277-1292, August.
    • Handle: RePEc:wly:riskan:v:32:y:2012:i:8:p:1277-1292
    DOI: 10.1111/j.1539-6924.2011.01611.x
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    References listed on IDEAS

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    Cited by:

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    3. Xia Han & Ruodu Wang & Qinyu Wu, 2023. "Monotonic mean-deviation risk measures," Papers 2312.01034, arXiv.org, revised Aug 2024.

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