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Suppose $X$ and $Y$ are two random variables where $X$ SOSD* $Y$. Let $g(\bullet)$ be a monotonic function and $X'=g(X)$ and $Y'=g(Y)$. Under what conditions of $g$ is

$X'$ SOSD $Y'$?

I know if $g$ is linear, SOSD property is reserved. Is there any suff and nec conditions of $g$ that assures SOSD property ?

*second-order stochastic dominance.

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    $\begingroup$ Hi and welcome. Would you like to add a definition of SOSD to the question. I found it on wikipedia but this would make the question more self-contained. $\endgroup$
    – Richi W
    Jan 15, 2019 at 10:19
  • $\begingroup$ Echo to Richard, why not explicit define SOSD in mathematical sense? $\endgroup$
    – Gordon
    Jan 16, 2019 at 17:39

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