# stochastic dominance

• July 3rd 2012, 04:38 AM
sander
stochastic dominance
The random variable X is stochastically dominated by Y. Therefore, for k = 1,2,...
$E[X^k] < E[Y^k]$
Show
$\left|\frac{E[X^{k+1}]/E[X^k] }{ E[Y^{k+1}]/E[Y^k] } \right| < 1$
If needed, one can impose positivity of Y, continuity of X and Y, and/or finiteness of moments of X and Y.