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Aumann and Serrano's Economic Index of Risk for Sums of Gambles

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  • Li, Minqiang

Abstract

We study Aumann and Serrano's (2008) risk index for sums of gambles that are not necessarily independent. We show that if the dependent parts of two gambles are similarly ordered, or more generally positively quadrant dependent, then the risk index of the sum of two gambles is always larger than the minimum of the risk indices of the two gambles. For negative dependence, the risk index of the sum is always smaller than the maximum of the two risk indices. The above results agree with our intuitions well. For example, the result for negative dependence agrees with our intuition of risk diversification. Thus this result can be considered another attractive property of Aumann and Serrano's risk index.

Suggested Citation

  • Li, Minqiang, 2014. "Aumann and Serrano's Economic Index of Risk for Sums of Gambles," MPRA Paper 55697, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:55697
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    References listed on IDEAS

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    1. Robert J. Aumann & Roberto Serrano, 2008. "An Economic Index of Riskiness," Journal of Political Economy, University of Chicago Press, vol. 116(5), pages 810-836, October.
    2. Minqiang Li, 2014. "Aumann and Serrano's economic index of risk for sums of gambles," Cogent Economics & Finance, Taylor & Francis Journals, vol. 2(1), pages 1-5, December.
    3. Minqiang Li, 2014. "On Aumann and Serrano’s economic index of risk," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 55(2), pages 415-437, February.
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    1. Minqiang Li, 2014. "Aumann and Serrano's economic index of risk for sums of gambles," Cogent Economics & Finance, Taylor & Francis Journals, vol. 2(1), pages 1-5, December.

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    More about this item

    Keywords

    Risk index; Additive gambles; Subadditivity; Positive quadrant dependence;
    All these keywords.

    JEL classification:

    • A10 - General Economics and Teaching - - General Economics - - - General
    • C00 - Mathematical and Quantitative Methods - - General - - - General
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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