Suppose that individuals with state-independent and risk-averse tastes insure each other through state-contingent trades.If there is no aggregate risk, the competitive equilibrium price will then result in actuarily fair insurance terms.

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Actuarily fair insurance terms mean that the premium paid by an individual is equal to the expected value of the payout received in case of loss. When individuals with state-independent and risk-averse tastes insure each other through state-contingent trades, they are essentially engaging in risk sharing. If there is no aggregate risk, meaning that each individual's probability of loss is uncorrelated with the probability of loss of all other insured individuals, then the competitive equilibrium price will result in actuarily fair insurance terms. This is because in the absence of aggregate risk, the total payout by all insured individuals will equal the total premium paid, and each individual's premium will be equal to their expected payout, making it actuarily fair.

Suppose That Individuals with State-Independent and Risk-Averse Tastes Insure Each