The Law of Large Numbers explains why it is unlikely that the actuarially fair premium for an insurance policy will be the same for a small start-up firm as it will be for a large employer such as a university.
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The Law of Large Numbers states that as the number of trials or observations increases, the average outcome will tend to approach the expected value or the true population parameter.
In the context of insurance premiums, actuarially fair premium is the price that is calculated based on the probability of the insured event occurring and the potential cost of the event for the insurer. Generally, actuarially fair premiums are determined using statistical data, which assumes that a large number of similar events are occurring.
For a large employer like a university, there are typically a lot of individuals covered by the insurance policy. This means that the insurer has access to a large pool of data, which allows them to make accurate predictions about the likelihood and cost of potential claims. Therefore, the actuarially fair premium for a large employer can be determined more accurately.
However, for a small start-up firm, there may be a limited number of individuals covered by the policy, resulting in less data available for accurate predictions. This can lead to a higher degree of uncertainty and variability in the potential claims, making it more difficult to determine the actuarially fair premium accurately.
In summary, the Law of Large Numbers explains why it is unlikely that the actuarially fair premium for an insurance policy will be the same for a small start-up firm as it will be for a large employer such as a university. The availability of a larger pool of data for the insurer to make accurate predictions and determine the premium is a key factor in this difference.