What shall I do with a student who self-plagiarized large parts of one of his previous work (for another class and another professor) for my own assignment (without stating it)?
Is it fair, considering he obviously chose to work on the same topic but without telling me that it was the case? I guess it happens all the time among students, to "recycle" like this...
My own opinion is that from the standpoint of generating grades, you either deal with plagiarism officially, or not at all. If you don't intend on adjusting grades, you might simply tell the student that this is wrong. If you do plan on issuing penalty, check with your school's academic honest policy, both to make sure that this self plagiarism is well described (it is in mine), and for what your next actions need to be.
You might use this as a cue to beef up the academic honesty sections of your syllabi to include this issue, so it is entirely unambiguous in the future.