26 Jan 2017 Aleatory Contract –. Insurance contracts are aleatory, which are contracts where the money relinquished by each party is not equal. For example, The second type of aleatory contract is where each party takes on a defined level of risk exposure, which is the consideration of the engagement of the other. For example, when a person buys an annuity, they take on the risk of losing the money in the case of their death soon after. Because most insurance contracts are aleatory contracts, it is always possible that an insurer may never have to pay policyholders any money whatsoever. For example, if a person buys a health insurance policy and then never visits the doctor or gets injured during the policy period, the insurer may collect premiums and never pay the insured without violating the contract.