1.3.7: Insurance

The insurance industry was one of the first large sectors that had a major dependence on at least the idea of uncertainty. The concept of insurance is quite old and is really a form of wagering. An individual might be afraid that an expensive adverse event might occur in the next year. A well-capitalized business associate recognizes the potential of this adverse event but is of the opinion that the event is very unlikely to occur. With this realization the two individuals enter into a business agreement. The individual will pay the business associate a set fee that is much smaller than the potential cost of the adverse event. The agreement is then that if the adverse event occurs, the business associate will cover the cost of the event, thus protecting the individual. However, if the event does not occur, the business associate will keep the fee. Hence it is a kind of a bet. The business associate is essentially betting that the adverse event will not occur, in which case they will get to keep the fee they charged the individual. The individual is essentially betting that the adverse effect will occur, in which case the cost associated with the adverse event is covered.

The most common modern application that most people are familiar with is automobile insurance. In the United States most automobile owners are required to have some minimal type of insurance to cover damage that that might be incurred due to accidents. In most cases the minimum type of required insurance is known as liability insurance, which will pay the cost of injury and damage incurred by the automobile owner, thus protecting the public. In this case the insurance company is betting that you will not have an accident over the coverage period, but in the case that you do, you are covered by the company.

Insurance has a history reaching back to roughly 3000 BCE, with early applications associated with marine insurance against losses of ships or their cargo in places like China and the Middle East and later in the Roman Empire (Dewan 2008; Vaughan 1997). Insurance became far more sophisticated and by the 15th century in Europe, specialized types of insurance were developed. The development of property insurance was precipitated by the Great Fire of London in 1666. In 1681, Nicholas Barbon and his associates established the first fire insurance company to homes (Dickson 1960). Around the same time Edward Lloyd’s coffee house became the meeting place for parties in the shipping industry and those willing to underwrite such ventures, which eventually led to the establishment of the now famous Lloyd's of London. By the 18th century, life insurance policies were being offered by the Amicable Society for a Perpetual Assurance Office, founded in London in 1706. The advent of accident insurance can be traced to the Railway Passengers Assurance Company, which was formed in 1848 in England to insure against fatalities on the railway systems.

Statistical methods allow insurance companies to assess the risk incurred by taking on a policyholder. This risk assessment is then used to determine how much the customer should pay as a premium. It is a well-known statistical property that if insurance companies can effectively spread their risk over many clients, the premiums paid by policyholders will be relatively small when compared to the possible losses by the policyholder. It is this property that makes insurance appealing to those who purchase it; for a relatively small premium they can guard themselves against large catastrophic losses.

The assessment of risk in insurance is based on very large sets of data gathered by the insurance company on the outcomes of previous policyholders and your own previous history. If you have been covered for a long time without any claims on your policy, then this is an empirical indication that the amount of risk associated with your policy is low. To set your rate the insurance company will consider that history along with the risk associated with other policyholders who have a similar profile to you. Other data is also considered. For example, a homeowner who lives in an area that is prone to catastrophic weather events has increased risk as the likelihood of a claim for home damage due to a storm is larger. Similarly, other aspects of your home may decrease risk, such as burglar and fire alarm systems that automatically contact emergency services in the event of an alarm.

Life insurance is based largely on what are known as life tables, which were a logical consequence of the “Bills of Mortality” complied in the 17th century in England. These publications listed and enumerated the number and types of deaths during a year in a particular area (David 1998). A life table is an estimate of the probability that an individual of a given age will live for another specified time. These tables are usually specific to gender and other factors. The estimates of the probabilities can, in principle, be based on looking at historical data. For a simplified example consider a woman who is 40 years old, and you wish to know the probability that that that individual is still alive at age 60. In principle, this probability can be estimated by looking at the proportion of women who were 40 years old 20 years ago and are still alive today. Modern methods use large sets of data on mortality and its causes along with statistical modeling techniques to produce these estimates. These estimates are the basis for setting life insurance rates as well as ensuring that commercial and public retirement plans remain solvent.