I have a suggestion for people traveling in Europe or anywhere else, who have their purses snatched while they are in their cars. If the car has seat belts, why not hook the purse strap around the seat belt lock before fastening. In that way, the purse is in the middle of the car, not quite so visible, and a little more difficult to snatch. If a thief leans over to grab it, you can always knee him.
This is also an effective way to keep the purse from sliding away from you when you're driving alone.