Context: insurance, risk theory, marketing

Premiums are moneys paid by one party (the insured) to another (the insurer) as part of a contract whereby the insurer will compensate the insured in the event of loss generated by a particular risk. Thus if the risk is death, then the premiums will be paid for a life insurance policy.

What is most interesting is how the premiums are determined.

# In Theory...

Mathematically, a premium principle is a function that transforms a random variable R (the loss) into a deterministic positively-valued number Π(R). This function has to satisfy certain properties, such as the premium for a deterministic loss (i.e. R is of a degenerate distribution), is the loss itself, and that premiums are subadditive.

There are several functions that can be used as premium principles. Theoretically the simplest is the expected value principle, where Π(R) = (1 + λ) E(R), with λ being a risk loading to prevent ruin in cases of catastrophic claims.

# In Practice... Pricing of insurance products are driven by marketing pressures. Nobody is going to buy your policy if it is more expensive than others. So usually the marketing department will determine the most appropriate premiums to charge, and it is left to the risk managers (usually the actuaries) to figure out a way that would ensure that the company does not ruin.

A grade of unleaded gasoline, usually with an (R+M)/2 method octane rating of 93. It usually costs 10-20% more than the 87 octane regular grade. This grade of gasoline is recommended for most sports cars, Volkswagens, luxury cars, and any other car with a high-compression engine. Also, running forced induction without premium gasoline is insanity.

Running this type offuel on a car that does not need it will not damage the car, however, it will not boost power or fuel economy either (you will just be wasting money buying a more expensive fuel). Running a lower grade of fuel on cars that need premium will only really harm cars without ECM systems (i.e. really old cars before the 80's). On cars with ECM systems, fuel economy and performance will suffer, but the car will still run without damage.

Pre"mi*um (?), n.; pl. Premiums (#). [L. praemium, originally, what one has got before or better than others; prae before + emere to take, buy. See Redeem.]

1.

A reward or recompense; a prize to be won by being before another, or others, in a competition; reward or prize to be adjudged; a bounty; as, a premium for good behavior or scholarship, for discoveries, etc.

To think it not the necessity, but the premium and privilege of life, to eat and sleep without any regard to glory. Burke.

The law that obliges parishes to support the poor offers a premium for the encouragement of idleness. Franklin.

2.

Something offered or given for the loan of money; bonus; -- sometimes synonymous with interest, but generally signifying a sum in addition to the capital.

People were tempted to lend, by great premiums and large interest. Swift.

3.

A sum of money paid to underwriters for insurance, or for undertaking to indemnify for losses of any kind.

4.

A sum in advance of, or in addition to, the nominal or par value of anything; as, gold was at a premium; he sold his stock at a premium.