Expectation of a function of a normal distributed r.v.

Hallo everybody,

is there any chance to compute the following expectation explicitly? (I don't think so. Am I right?)

where

is a normally distributed r.v.

a constant

constants

Actually, I want to maximize the expectation w.r.t over the interval ( is non-random). I know that the maximum exists since is concave and the interval compact. But does anyone has an idea how to compute the maximum?

Thanks in advance

Re: Expectation of a function of a normal distributed r.v.

is an integer? if so you can expand your brackets and end up with a bunch of lognormal variables (the expectation of these is a standard result)

Re: Expectation of a function of a normal distributed r.v.

Thank you for your answer.

No, is not an integer. In most of my applications is between and

Re: Expectation of a function of a normal distributed r.v.

i dont know then, i suggest you lookup the derivation of the moments of a lognormal distribution since those are similar to what you need to do.