Discuss the relationship between risk and insurance.

Risk is the exposure to uncertainty. An insurance policy is an exchange of a certain loss (the premium) to have another party (the insurer) absorb all or part of the negative consequence of being exposed to that uncertainty.

For example, you have virtually no risk of dying in an airplane crash if you do not get in an airplane. You are not exposed, other than that a plane could fall on you. Likewise, if you jump out of an airplane without a parachute, there is no risk. You have all the exposure in the world, but it is certain that you will be killed. There may be some trivial risk that you live but it is so small that it can be ignored.

You need two things, uncertainty and exposure. Life insurance is a good example, you know for certain that you will die, you do not know when. The insurer covers you against premature death. Its reverse, the immediate annuity, covers you against living too long and running out of investment resources.