pros and cons of insuring your engagement ring under homeowner's insurance?

If I get my engagment ring from a pawn shop, have it appraised, is it ok to get it insured under our renter's or homeowner's insurance company?

What if you don't rent or own a home right now? Can you buy the ring now and then when you buy a home/rent an apartment, can you get it insured later??? how does this work?

You can buy a policy just for your ring. I have one and it doesn't cost much.