Insurance makes wealth grow faster

TL;DR

This paper proposes that viewing insurance contracts through the lens of time-average wealth growth, rather than expectation value, resolves classical puzzles about their existence without requiring utility functions or asymmetric information.

Contribution

It introduces a novel approach to understanding insurance by focusing on time-average growth rates, eliminating the need for utility-based or information asymmetry assumptions.

Findings

Insurance contracts increase time-average wealth growth for both parties.

The classical puzzle is resolved by considering non-ergodic wealth dynamics.

Business success correlates with both parties experiencing faster growth.

Abstract

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.