MyTwoToodles, please ignore the advice by alanRow, which is wrong on two counts:
1. If the purse is under your arm and the strap is on your shoulder, you will *not* be dragged along the road. If the strap is across the body, you might be.
2. The whole shoulder/body discussion is completely hypothetical. In northern Italy, *no one* will try to grab your purse, certainly not from a moving vehicle. At worst, they might try to pickpocket you. Pickpocketing is *not* a violent crime; most people who are pickpocketed never notice it at the time.

I guess european women are not allowed at their shops ...
http://www.intimissimi.it/#/Home?lang=en