# Transformation of random variables and second-order stochastic dominance

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.

• 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. – Ric Jan 15 '19 at 10:19
• Echo to Richard, why not explicit define SOSD in mathematical sense? – Gordon Jan 16 '19 at 17:39