In the other words, there is a cost function `f(p)` which is the amount of money to spend in order to prevent the fatal risk of probability p. For low enough p

In the other words, there is a cost function `f(p)` which is the amount of money to spend in order to prevent the fatal risk of probability p. For low enough p this function can be linearly approximated, and we named the value of `f(1)` under this approximation as the value of statistical life only for convenience. (In reality `f(1)` or even `f(0.01)` is not defined, and the true value is mostly determined after the fact.)