Breaking News Team:  Absolutely it's best to give up one's purse (or, I guess, in Chico's case, wallet or briefcase), preferably by throwing it as far away from you as possible, then run like the wind away from the "perp" while he's running to catch up with the loot. 

Reminds me of the story of the mother (an older woman) of a friend of ours who'd left her house, locked the door, turned around to find a couple of hoodlums trying to take her purse.  Instead, she began yelling at them and hitting them with the purse, repeatedly, until they just ran off.  She was a little shaken, but she was determined that those little jerks were not going to get her purse.  She'd lived in Germany during WWII, had not had an easy life, and was not one to be messed with. 

 Take it from someone who was dumb enough to stick her hand in her Labs mouth to try and pry the Westie out of her jaws.  I'd have held on to my purse.  Some of us may not be too bright but we ain't skeered.  Once the adrenaline takes over, rational thought sometimes goes out the window.

My advice however, is give it up on the purse.  That purse isn't worth you losing your life.

 eric, it is so easy for you to sit at your computer and say what this lady should have done. Sometimes instinct just kicks in. In instances like this, a person doesn't always have time to think things out. They just react. Some people fight back instead of just rolling over. I have a feeling I know which one you would do...

 You got it Bartley!!!  That's what I'd be doing!!!