Thanks for explanation, Mr. David. Your forum is a real addition to me.
" We use may/might + have+ past participle to talk about possible events in the past, present and future" " Advanced grammar in use third edition" P.34 Section E.
Ex. " His maths might have improved by the time the exam comes round."
Why not might have lived works here. I totally agree might be living is best as it expresses a trend in the not too distant future. But may you give me stronger reasons to omit might have lived as a probable answer?