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SYEF: Symposium Statistical Physics of Economic and Financial Systems

SYEF 1: Statistical Physics of Economic and Financial Systems

SYEF 1.5: Invited Talk

Thursday, March 21, 2024, 11:45–12:15, H 0105

Ergodicity Economics and the Insurance Problem — •Benjamin Skjold, Ole Peters, and Colm Connaughton — London Mathematical Laboratory

A key puzzle in economic theory is the spontaneous emergence of insurance arrangements. Here, entities agree on a contract whereby the buyer pays a known fee, and the seller (often an insurance firm) pays an uncertain payout contingent on some future event. Modelling this contingent payout as a random variable, it is clear that whatever fee is agreed upon, either the buyer or the seller will necessarily lower its expected financial future wealth by signing. Yet, such contracts have commonly been signed voluntarily, at least since Babylonian times. The solution to this puzzle which we explore is ergodicity economics: while it is true that one entity always lowers its expected wealth, expected wealth is often less relevant to the signatories than time-average growth. When, as is usually the case, the underlying wealth dynamic is not additive, the growth rate of expected wealth and the time-average growth rate of wealth differ. Time-average growth of wealth, as opposed to expected wealth, can increase for both parties, which resolves the basic puzzle.

Keywords: Insurance; Ergodicity Economics; Cooperation; Intermittency