Related Topics
There are a handful of topics that are loosely related to insurance that I wanted to separate from the information above:
History
The history of insurance is largely trivia insofar as understanding its current incarnation, but some knowledge of the background may explain some vestigial weirdness that affects the present.
Primitive Forms
In a primitive sense, insurance existed in most human societies: a hunter who failed to catch would be fed by others in his tribe, generally with the understanding that he would be willing to share his catch with others when the situation was reversed.
Another primitive form of insurance was the public granary that arose in Mesopotamian culture (and later spread westward), in which farmers stored their grain in communal vats, and a share of that grain would go to the community in exchange for having his harvest thus protected.
The rise of feudalism is also reckoned to be a form of insurance, in which the vassals would provide tribute and support to a collective leader, who would use the collective resources of his vassals to protect their fief (and the tribute he paid to his own lord could be interpreted as a form of reinsurance).
Commercial Insurance
There were also risk-sharing practices in early commerce. Around 3000 BCE in China, merchants shipping goods down a river would share risk by dividing their goods among multiple barges, such that if one barge sank, each merchant would lose a little of their goods, but no one individual would lose everything.
Probably the earliest form of explicit insurance was recorded in the Code of Hammurabi (1750 BCE), which provided a merchant who received a loan to fund a shipment the option to pay an additional sum in exchange for being forgiven the loan if the shipment was stolen.
Commercial insurance is traced back to the seventeenth century shipping trade, when ship owners, captains, and merchants gathered in coffee houses (such as that of Edward Lloyd in London) and formed a more systematic method of insuring cargoes and ships to mitigate the risk of having one's vessel and cargo lost at sea.
Individual Insurance
In Greece, "benevolent societies" formed, which later became guilds in the Middle Ages, to which members paid dues for membership, and one of the benefits of membership was specific forms of financial assistance in times of misfortune, or taking care of a tradesman's family in the event of his death.
The church in the middle ages provided a similar benefit to some of its parishioners: a wealthy individual would grant monies to the church, whether in installments over time or as a lump sum, for the assurance that the church would provide an income for his family after his death.
Homeowner's insurance came into being around the seventeenth century, after the Great Fire of London. Individuals with experience selling and buying shipping insurance at the same time saw its application to housing and the risk of fire. Over time, additional coverage, specific to perils, was conceived, and these were then bundled into single policies that insured against multiple specific risks (fire, storms, floods, etc.).
Actuarial Science
"Actuarial Science" is currently the preferred term for the practice of using statistical models to predict risk and financial data to assign value to it. The practice has taken a giant leap forward in current years, with the advance of computer technology ... so much so that I can't find a clear explanation of how it is done, just the names of theories, models, and software packages that are used.
Traditionally, actuaries were largely limited to predicting losses based on regular patterns over time - which is generally effective when the future follows the trends set by the past, and when the risks faced by the insured are largely independent of one another. This is generally quite reliable, until a catastrophe occurs - an unpredictable event that affects a large number of policyholders at the same time.
Because of the significant numbers of major catastrophes in the past few decades (wildfires, mudslides, and earthquakes in the west; tornadoes and flooding in the central states; and hurricanes on the eastern seaboard), which defy regression analysis, the need for a better catastrophe prediction model is becoming increasingly clear.
In the end, actuarial science is a necessity of insurance, but understanding it in depth is probably not necessary. From a practical perspective, just know that it is used as a method of estimating risk, as an input to the calculation of premiums.
Risk Management
Insurance is a method of risk management: a company or individual pays an affordable fixed sum on a predictable schedule to shield themselves against the possibility of having to pay an unpredictably large sum in case of an unlikely event. However, risk management does not subsume insurance.
"Risk Management" has emerged as a profession that seeks to define organizational policies and procedures to minimize the potential for exposure, generally with a goal of controlling or decreasing the organizations' insurance expenses. The establishment (and maintenance) of an RM department is justified by the perceived savings: if the savings exceed the expenses of an RM department, it makes sense to have one. Otherwise, RM responsibilities can be assigned to the appropriate personnel in various departments, primarily properties, legal, and human resources.
There's more to be said on the subject, and RM departments serve additional functions in many organizations, but the information above covers the basics insofar as they are germane to the topic of insurance.
Self-Insurance
The term "self-insurance" is not an industry standard term, and the practices to which it refers vary.
In most instances, self-insurance refers to a method of expense planning. While its function is similar to that of insurance (small amounts paid over time toward large expenses), it is not the same as actual insurance (though it may be used as a substitute for it).
For example, if a company owns twenty forklifts, the operating expenses of each lift may include a line item for mechanical failures that does not represent an actual cost, but contribution to a pool of funds that will be used for those lifts that happen to need repairs beyond the scope of typical maintenance.
In some instances, such self-insurance is accepted as equivalent for actual insurance that may be legally required to conduct business in a certain location.
Another practice termed "self-insurance" is nonprofit organizations offering conditional benefits to members as a benefit of paying membership fees - however, unless the coverages and terms are defined and the correlation of premium to coverage made explicit, it is not actual insurance, not can it be enforced (such an arrangement fails the common-law tests of consideration and specificity).
Annuities
An "annuity" refers to a payment made in regular installments, which is how some life insurance policies pay their settlements (an annual pension to a widow rather than a lump sum). While annuities are considered "investments," they are sold through, and managed by, insurance companies instead of investment brokers.
The annuity product evolved from life insurance, such that a person could set up a pension for themselves by making payments in advance to a life insurance policy that "endows" over a period of time. It is also common for an annuity to include life insurance provisions, such that if the CQV dies before paying the premiums, the policy will still pay out to their beneficiaries.
Finally, annuities are generally considered to be a very poor choice for the majority of investors - the return on investment is pathetic, and it's a very profitable item to sell (which is why they're still pimped by insurance companies).
However, individuals whose nest egg is barely enough to squeak by, such that any fluctuation in interest rates would have dire consequences of their income, are often better served by an annuity.
Annuities are also an effective shelter for bad debtors, as it is has the legal protection of life insurance. So unlike investments, the "value" of an annuity is protected from seizure by creditors.