The Mathematics of Money

(Darren Dugan) #1

Copyright © 2008, The McGraw-Hill Companies, Inc.


Policy Type What It Covers

Disability Provides fi nancial benefi ts if you become disabled. Some provide benefi ts only if you
are unable to work at all, while others provide benefi ts if you are unable to work at
your usual profession. Benefi ts are often set as a percent of predisability income.
Earthquake Covers damages caused by earthquakes, which is not covered by most homeowner’s
insurance policies. May be purchased as a separate policy, often connected to a
homeowner’s policy.
Flood Covers damage due to fl oods, which is not covered by homeowner’s insurance policies.
Health Also called medical insurance, health insurance covers the cost of medical treatment.
Health insurance policies may be comprehensive, covering most types of medical
costs, or may only cover specifi c types of medical treatments. Dread disease policies
provide coverage only for a specifi c type of diagnosis.
Homeowner’s Covers damage to your home and property due to fi re, weather, theft, and many other
causes. Also usually includes coverage for liability for injuries visitors suffer on your
property. Homeowner’s policies do not cover damage from fl ooding or earthquakes
and may have other exclusions as well, such as limits on the amount of coverage
for jewelry or computers. Policyholders may be able to purchase riders, additional
coverage for risks that would otherwise be excluded.
Liability Covers fi nancial losses due to claims and lawsuits against an individual or business
for injuries or other damages for which it may be held fi nancially responsible. Some
policies may cover only certain types of liabilities, while general liability insurance
covers a broad, but not necessarily all-inclusive, range of possible claims. Individuals
often have liability coverage through their homeowner’s and auto insurance policies;
businesses usually purchase separate liability policies.
Life Pays a fi nancial benefi t to your family (or others that you specify) in the event of your
death.
Professional liability Professional liability covers liability for damages to others while working in your
profession. Malpractice insurance, most commonly associated with physicians, is a
type of professional liability coverage.
Property Similar to homeowner’s insurance, but covers property such as business offi ces or
rental property. May not include liability coverage as homeowner’s does. Property
insurance may also be issued for specifi c types of risks, such as fi re insurance.
Renters Similar to homeowner’s, but does not cover damage to the property.
Umbrella Umbrella policies are purchased in connection with auto and homeowner’s insurance.
Umbrella policies offer coverage for liability claims that exceed the coverage limits on
auto and homeowner’s policies.
Unemployment Provides income when you lose a job. Unemployment insurance is a government
program; it is not provided by insurance companies.
Workers’ compensation Provides compensation for injuries to a business’s workers sustained while on the job.

Insurance and the Law of Large Numbers


Before talking more about insurance itself, we need to understand the mathematical
principles that make insurance work. The most significant is the law of large numbers. The
law of large numbers assures us that, while it may be impossible to predict whether or not a
random event will happen in any individual situation, it may be possible to make a reason-
able prediction about how may times it will happen over a large number of situations.
One familiar example may help to illustrate this. When you flip an ordinary coin, there
are two possible results: heads or tails. There is a 50/50 chance of getting either heads
or tails on any given flip, so we would expect the result should be heads half the time
and tails the other half of the time. Now suppose you flip a coin twice. This suggests
that one flip should come up heads and one should come up tails. This may happen, but
you certainly wouldn’t be all that surprised if both flips came up heads or both came up
tails. With just two flips, everyday experience tells us not to expect the proportion of
heads or tails to necessarily be exactly 50%; 0% or 100% are both completely reasonable
outcomes.

13.1 Property, Casualty, and Liability Insurance 525
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