  Voluntary insurance contracts constitute a puzzle because they increase the
expectation value of one party's wealth, whereas both parties must sign for
such contracts to exist. Classically, the puzzle is resolved by introducing
non-linear utility functions, which encode asymmetric risk preferences; or by
assuming the parties have asymmetric information. Here we show the puzzle goes
away if contracts are evaluated by their effect on the time-average growth rate
of wealth. Our solution assumes only knowledge of wealth dynamics. Time
averages and expectation values differ because wealth changes are non-ergodic.
Our reasoning is generalisable: business happens when both parties grow faster.

Risk Management;Economics