Before revision: We present a mathematical solution to the insurance puzzle. Our solution only uses time-average growth rates and makes no reference to risk preferences. The insurance puzzle is this: according to the expectation value of wealth, buying insurance is only rational at a price that makes it irrational to sell insurance.
After revision: Voluntary insurance contracts constitute a puzzle because they increase the expectation value of wealth, buying insurance is only rational at a price that makes it irrational to sell insurance.