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patrick
Posts:
3
From:
France
Registered:
7/13/17


Supermodularity preserved by Expectations?
Posted:
Jul 13, 2017 4:26 PM


Consider a function $f(a,b)$ that is supermodular in $(a,b)$, increasing in both variables and convex. Consider a random variable $\tilde{a}$, We shall denote by $E_a$ the expectations of $f$ wrt to $\tilde{a}$, assumed to exist.
Is it true that $E_a(f(\tilde{a},b)$ is supermodular in $(E(\tilde{a},b)$?
Thanks in advance for any hint!



