  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.
