It is true that one cannot describe every detail and circumstance of any hypthetical senario. Taking just the information that you have said my answer is this:
In a split second I have to make the a decision. I can either surrender or fight. Fleeing in such a senario isn't really an option. No matter what I do the outcome will be that I will either live or I will die.
I will very calmly tell the BG something like this: "I'll give you everything. You don't have to shoot me, it's not worth it. I'll give you everything and I'll go home and you'll walk away with my money and valuables. I'm going to reach down and give you my wallet"
At this point I slowly move my right hand down to my wallet. Once my hand is as close to my weapon as it can be without letting the BG know it's there I explode with movement. I quicly turn to and move to the right, knocking his weapon to the left with my elbow or arm. With my left hand and/or one of my legs I push and/or kick him as far away as possible while drawing my firearm. I immediately take aim. If I have time I tell him something like "Drop the gun or I'll shoot you and kill you." If he doesn't do as I tell him to, or as soon as the muzzle on his gun begins to move in my direction, or if he makes any kind of movement I take as hostile, I open fire. I shoot until his gun contacts the ground or I run out of ammo.
That's the best answer I can give. I don't surrender to his threat because of three main reasons:
1. If he gets my gun that will only give one more BG the means to kill an innocent person. I'd die to keep that from happening.
2. He's a BG and I'm really sick and tired of BG's. I really wish I lived in a world where I didn't feel the need to have a firearm. I wouldn't have guns if none of the BG's had them.
3. I've defended myself from lethal force using hand to hand combat before. I know exactly how I react in such situations and I feel cofident I can take the average BG quick enough and long enough to pull my weapon. If the BG is close that close to me, he's close enough for me to engage him and I believe that because of my experiences and training I have the upper hand in that situation.
I'll be the first to admit that if the BG were to engage me using tactics that gave him the upper hand, and if I believed he would shoot me if I resisted and would let me live if I didn't, I would gladly hand over whatever he wanted. Until it came to my gun that is. I am a firm believer I am responsible for all of the firearms that I own, and every single bullet that goes through it's barrel. The only way to relinquish that responsibility is to transfer ownership of the firearm to someone who I believe to be just as mature and responsible as I am (another good guy). I'll die trying to keep my guns out of the hands of rapists, murderers, etc.