Ask most people how much they value their life and they will inevitably say "an infinite amount." That's what my girlfriend told me the other day (generated from a conversation I've forgotten the origins of). "This cannot possibly be true," I said. "You take risks."
Mathematically, here's how it works. The expected cost of any activity under uncertainty is the likelihood of the event times the cost if the event occurred. A fifty percent chance of losing $200 means that the expected cost is $100. For any activity there is a probability you will die, or lose that life you value at an infinite amount. Thus, it's an infinite cost no matter what you multiply it by, no matter how risky the activity is. Since you have to do something to stay alive, you should always choose the least risky activity, no matter how much you might value the alternative because of the costs of that activity are infinite.
That people value their life only because they value what they can do with it doesn't change the math. In life, there are always options. You can watch TV or skydive: both are valuable to you and while the former might be more fun after 8 hours of TV a day, it is still too costly. But people still skydive.
They also show their finite value of their own life in other ways. People speed, jaywalk, ignore check engine lights, confront rude people (who might kill them out of anger), forget to check smoke detectors, travel to foreign countries, and eat unhealthy food. When we change our estimations of how dangerous (or safe) an activity is, we change our behavior. But if we valued our life infinitely, that shouldn't change anything (as the costs would come out the same regardless of the probability of death). Clearly, the costs to risking your life are lower than you might think.