Is it possible to automatically sign in to the Mac App Store? Each time (at the beginning of the session) I buy or update an app in the mac app store I have to sign in.
I want to be automatically signed in, like I am in the iTunes Store. 

I couldn't find any "remember password in keychain" option.
Did I miss an option somewhere? Or is there any way so I get signed in automatically?
No, this option doesn't exist. (Perhaps because it would be to some extent a security risk.) You might remain signed in for a short period of time, but you can't automatically log yourself in.