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Stochastic superiority

Author

Listed:
  • Liqun Liu

    (Texas A&M University)

  • Jack Meyer

    (Michigan State University)

Abstract

This paper introduces a definition of stochastic superiority. One random variable is stochastically superior to another whenever it stochastically dominates the other after the risk in each random variable has been optimally reduced. Stochastic superiority is implied by stochastic dominance, but the reverse is not true. Stochastic superiority allows more pairs of random alternatives to be ranked, and efficient sets to be smaller. A very strong sufficient condition for stochastic superiority is demonstrated to also be necessary when preferences are risk averse. This condition provides a relatively easy way to conduct stochastic superiority tests. As an alternative to “almost stochastic dominance,” stochastic superiority also provides a natural solution to the “left tail problem” that arises often when comparing random alternatives.

Suggested Citation

  • Liqun Liu & Jack Meyer, 2021. "Stochastic superiority," Journal of Risk and Uncertainty, Springer, vol. 62(3), pages 225-246, June.
    • Handle: RePEc:kap:jrisku:v:62:y:2021:i:3:d:10.1007_s11166-021-09362-9
    DOI: 10.1007/s11166-021-09362-9
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    References listed on IDEAS

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    More about this item

    Keywords

    Stochastic dominance; Almost stochastic dominance; Set dominance; Left tail problem; Self-protection;
    All these keywords.

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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