There are a lot of ways to view insurance.  The agent sees it as a service he provides, and a product to sell. A claims adjuster sees it as paying the customer for the loss covered by the contract.  Lawyers see insurance as a special kind of contract.

Some early insurance activities were set up by people wanting to manage their risk.  For example, some early workers placed a small amount of money into a fund, which was given to the widow of the worker in the event the worker was injured or killed on the job.  Over the years, these funds, or pools, were replaced by companies who handled the funds – the first insurance companies.  The mathematics did not change, i.e. small deposits by many paid for the losses of the few.

These funds can survive only if the amount of money going into them (in the form of premiums) is at least as much as the money flowing out of them to pay for losses and expenses. 

As the companies learned that different participants brought a different likelihood of loss to the fund, they started demanding different contributions – low risk participants paid low amounts, and high risk participants paid higher amounts.  People with similar risk are placed into groups, called classes, for the purpose of charging them an appropriate premium.  For example, people with no accidents are put into a group and charged a lower premium than people with many accidents.

Underwriters determine the class to which each person is assigned.  They accept or reject new members of the pool, and kick out participants whose risks are determined to be too great for any of the classes.  In this manner, they keep the fund solvent, and keep down the costs for the members.

The person who determines how much the premiums should be for each class is called an actuary. An actuary is a person skilled in risk analysis and mathematics who determines how much risk different members of the fund bring to the fund.  (Members are also referred to as "insureds.")  For example, an actuary determines that people who live along the San Andreas Fault should pay more for earthquake insurance than people buying earthquake insurance who live in Kansas.  At the same time, they determine that people who live in Kansas should pay more for wind and hail insurance than people who live in California.  How much each group pays verses the other is a long and complicated mathematical problem.

The actuary attempts to keep the cost low enough to be attractive to the customer, yet high enough to keep the fund, that is the company, solvent.  Actuaries buy insurance too, and are interested in finding ways to keep the costs down, while keeping their companies alive.