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Mathieu Clement
Mar 20, 2021

Expected value (exp(x)-1)^a

in Math Problems

Hello,


I love your channel and your community. Thanks a lot for your work!



I'm stuck with an integral since a while and I'm getting obsessed :)


integral_0^infinity (exp(x)-1)^a exp (-1/2 * ((x-mu)/sigma)^2) dx

0<alpha<1


(expected value of (exp(x)-1)^alpha where x follows on normal distribution mu sigma)


I've managed to find an approximation (see attachment) and it's sufficient for my need but I feel like the exact solution exists. I've learned a lot of new techniques when trying to solve this integral :)


Do you have some tips?


Thanks,

Regards,

Mathieu

Expected utility value
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