Insurance premiums are calculated using variables like age and health history and involve statistics and the Law of Large Numbers. These premiums are determined by predicting the risk of events for a large pool of insured individuals. Moral hazard is when insurance influences the insured's behavior, potentially increasing the risk.
The concepts that are applied in real life, including the calculation of insurance premiums for different types of insurance such as health, car, house, and life insurance, involve the use of statistics, probability, and the Law of Large Numbers. Insurance premiums are regular payments made by policyholders to insurance companies, which are priced based on the probability of certain events occurring.
For each type of insurance, these variables might include age, health history, driving record, home location and construction type, lifestyle, and occupation among others. Regarding the average benefits paid versus the average premiums, it is more about the latter where the average benefits are meant to equal the average premiums paid across the entire pool of policyholders, not on an individual basis.
An actuarially fair insurance policy would be one where the premium reflects the true risk of the events covered. The problem of moral hazard arises when the presence of insurance alters the behavior of the insured, leading to a greater chance of a claim being filed.
Furthermore, insurance companies use the Law of Large Numbers to predict the occurrence of events for a large group and thus determine the premiums. The larger the pool of policyholders, the more accurately the insurance company can predict the overall risk and spread the cost among all insured, making insurance a feasible financial product.