Lecture 4: Insurance
The Archetypal Risk Management
Institution
Fundamental Insurance
Principles and Issues
• Risk Pooling is the source of all value in
insurance
• Moral Hazard dealt with partially by
deductions and co-insurance
• Selection bias dealt with by group policies,
by testing and referrals, and by mandatory
government insurance
Risk Pooling
• If n policies, each has independent
probability p of a claim, then the number of
claims follows the binomial distribution.
The standard deviation of the fraction of
policies that result in a claim is p(1  p) / n
• Law of large numbers: as n gets large,
standard deviation approaches zero.
Aristotle on Probability
• “To succeed in many things, or many times,
is difficult; for instance, to repeat the same
throw ten thousand times with the dice
would be impossible, whereas to make it
once or twice is comparatively easy.” (De
Caelo)
Earliest Known Description of
Insurance Idea
Anonymous letter to Count Oldenberg, 1609,
proposes that people pay 1% of value of home into
a fund, to be used to replace house after fire.
Writer says he(she) “had no doubt that it would be
fully proved, if a calculation were made of the
number of houses consumed by fire, within a
certain space, in the course of thirty years, that the
loss would not amount, by a good deal, to the sum
that would be collected in that time.
Insurance as an Invention
• Contract design, specifying risks, excluding risks
subject to moral hazard or selection bias.
• Definition of loss and sufficient proof of loss
• Mathematical model of risk pooling
• Collection of statistics on risks, and evaluation of
the quality of such statistics.
• Corporate or mutual form for the company
• Government verification of insurance company’s
ability to pay
• Government regulation of insurance
Invention of Insurance
• In ancient Rome, burial societies and
bottomry. (Burial insurance still a factor in
less developed countries.)
• Actuarial science developed in late 1600s
• Modern fire insurance began in London,
insurance gradually spread around the
world.
Commercial Insurance
• Property & Casualty Insurance, In US premiums
paid 1997 $276 billion, $2760 per household
• Private Health Insurance: premiums paid 1996
$137 billion, $1370 per household
• Life insurance: In US, premiums paid 1997 $112
billion, or $1120 per household, 373 million
policies, with value of $13.2 trillion in US in
1997, $132,000 per household. 1620 US life
insurance companies.
Property & Casualty Insurance
Premiums, US 1997
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Automobile $132 billion
Homeowners $27 billion
Other liability $25 billion
Worker’s Compensation $24 billion
Commercial multiple peril $19 billion
Other categories
Origins of Insurance Demand
• Slow growth from 1660s of insurance
industry
• Regulation
• Mortgage institutions
• Public Education
Marketing of Insurance
• Mutual Life Insurance of New York in
1840s: Morris Robinson trains highly-paid
life insurance salesmen
• Equitable Life Insurance Association in late
1800s: Henry B. Hyde invents tontine life
insurance policy, sweeps the nation
• Whole life is successor to tontine
Types of Life Insurance I
• Term insurance: level term and annual renewable
term (premium increases)
• Whole life: guaranteed cash value builds
according to schedule (nonparticipating) or with
investment upside (participating). Government
subsidy: income on cash value is not taxed
• Variable life: no guaranteed cash value, policy
holder shifts investments among accounts
Types of Life Insurance II
• Universal Life: like whole life but also
gives policyholder flexibility over
premiums, unbundles cash value and
insurance. Can increase or decrease
premiums as needs change
• Variable universal life
• Survivorship (second to die) insurance
• Why the multiple forms? Marketing issues
US Government Regulation of
Insurance
• McCarran Ferguson Act 1945 delegated insurance
regulation to the states. Fifty different state
regulators.
• National Association of Insurance Commissioners
(NAIC) creates standardized suggested laws.
• In 1993 the NAIC adopted risk-based capital
requirements.
• Gramm-Leach-Bliley Financial Modernization Act
of 1999 allowed banks to affiliate with insurance
companies
Capital Requirements
• Insurance companies risk being unable to
pay if there are too many claims.
• Why don’t insurance companies define their
contracts so that they cannot fail to pay?
• Human factors engineering of financial
contracts.
Surplus and Reserves
• Statutory Surplus: Amount beyond reserves
that an insurance company has invested
• Reserves: An accounting entry, amount they
are thought to need to pay the claims.
Failures of Insurance Industry
• Whole life used to be stressed over term life
insurance. (universal life alternative)
• Benefits not indexed to inflation
• Life annuities not indexed to inflation
• Human factors behind these failures