Connection between higher order measures of risk and stochastic dominance

Alois Pichler
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Alois Pichler: Technische Universität Chemnitz, Faculty of Mathematics

Computational Management Science, 2024, vol. 21, issue 2, No 4, 28 pages

Abstract: Abstract Higher order risk measures are stochastic optimization problems by design, and for this reason they enjoy valuable properties in optimization under uncertainties. They nicely integrate with stochastic optimization problems, as has been observed by the intriguing concept of the risk quadrangles, for example. Stochastic dominance is a binary relation for random variables to compare random outcomes. It is demonstrated that the concepts of higher order risk measures and stochastic dominance are equivalent, they can be employed to characterize the other. The paper explores these relations and connects stochastic orders, higher order risk measures and the risk quadrangle. Expectiles are employed to exemplify the relations obtained.

Keywords: Higher order risk measure; Higher order stochastic dominance; Risk quadrangle; 62G05; 62G08; 62G20 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10287-024-00523-0

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