Standard Article

Axiomatic Measures of Risk and Risk-Value Models

  1. Jianmin Jia1,
  2. James S. Dyer2,
  3. John C. Butler3

Published Online: 14 JAN 2011

DOI: 10.1002/9780470400531.eorms0078

Wiley Encyclopedia of Operations Research and Management Science

Wiley Encyclopedia of Operations Research and Management Science

How to Cite

Jia, J., Dyer, J. S. and Butler, J. C. 2011. Axiomatic Measures of Risk and Risk-Value Models. Wiley Encyclopedia of Operations Research and Management Science. .

Author Information

  1. 1

    The Chinese University of Hong Kong, Department of Marketing, Faculty of Business Administration, Shatin, Hong Kong

  2. 2

    University of Texas at Austin, Department of Information, Risk, and Operations Management, The McCombs School of Business, Austin, Texas

  3. 3

    University of Texas at Austin, Department of Finance, The McCombs School of Business, Austin, Texas

Publication History

  1. Published Online: 14 JAN 2011

Abstract

This article provides a review of risk and risk-value models that lead to decision making by explicitly trading off between risk and value. We begin with a discussion of a preference-dependent measure of risk that is compatible with traditional expected utility theory, and therefore lends itself to an examination of how individuals perceive risky gambles as well as how they choose among them. Further, this risk measure can be the basis for generalizing models of decision making based on the intuitively appealing notion of trading off between risk and value. Based on the two-attribute expected utility axioms, this risk-value framework has much more flexibility in modeling preferences than the traditional single-attribute expected utility theory. Specifically, we describe three useful classes of decision models: moments risk-value models, exponential risk-value models, and generalized disappointment models. These decision models unify two streams of research: one in developing preference models and the other in modeling risk judgments. They can also provide prescriptive guidance for those people who are willing to deviate from the traditional expected utility preference models and make their decisions based on risk-value trade-offs, as in financial decision making.

Keywords:

  • risk measure;
  • risk-value model;
  • risk-value trade-off;
  • mean–variance model;
  • utility model