Insurance Flashcards
simplest form of insurance is
mutual insurance
mutual insurance
• When a member of a group is unlucky, gets helped out by the
other members
• Works in small long-term groups: hunter-gatherers, small
villages, early trade unions
• Small groups know each others risk profile
• Small groups can monitor each other’s behaviour
• And punish excessively risky behaviour
• Over the long-term, you know the gains and losses will
wash out
Modern insurance companies lose out on… but gain…
Lose out on a lot of informational advantages of small
groups
• But gain economies of scale, tailored products and easier
to transact.
Underinsurance
Caps on coverage
• Insurance will only pay off up to a maximum
amount
• e.g., in the US you had health insurance with
”life-time caps”.
• Coverage being denied
• Some customers may find it impossible to
find insurance at any price.
• Lack of insurance markets for bad decisions
Explanations for underinsurance
- Credit constraints
- Moral obligations/interest group
politics - Non-diversifiable risk
- Adverse Selection
- Moral Hazard
Credit constraints
People who simply cannot afford insurance, and
hence must bear the risk.
• Can be solved through either subsidies, or the
state providing insurance for free.
• Low income as limited liability:
• low-income/high-risk drivers may not see the
need to get insurance given that would never be
able to pay the full cost of any damage caused
anyway.
Moral obligations
Most of the civilized world sees healthcare as a
right: people will not be refused care, are not
asked for proof of insurance/income before
necessary treatment is started
• Thus can be a reason to underinsure.
• Same with for example flood insurance: in the
case of a bad flood the government usually pays
out anyway
• Regulatory solution: compulsory insurance if
you live in a flood prone area.
• Instead of moral obligation may also be lobbying
power
Non-diversifiable risk
• Insurance usually works with the “Law of large
numbers”: some lose, some don’t, insurance
company can predict the average number of
claimants.
• But for some risks, if they come to pass everybody
loses, so these events are difficult/ impossible to insure
• Global warming for example:
Moral hazard
When you are insured you may start taking more risk, resulting in more claims, higher rates and in the end making insurance unattractive for everybody but the biggest risk-takers
Adverse selection
• The highest quality customers (lowest risk) are
least likely to buy insurance, selecting themselves
out of the market.
• This makes the remaining pool more risky on
average, driving up prices.
• Higher prices drive out more high quality/low
risk customers, again increasing the average
riskiness of the pool, etc, etc.
• Similar death spiral, but now from the
customer side.
• Solution: compulsory insurance.
• Alternatively, insurers can design different
policies that separates different risk types
How does insurance work
- Risk pooling
- Risk spreading
- Risk transfer
Risk pooling
• When outcomes are independent, any single
outcome cannot be predicted, but the average
number of outcomes can.
• Example: coin flip. E(H) = 0.5n / n, Var(H) = p(1−p)/n
• Pooling many independent risks allows to
insurance company to treat the aggregate outcome
as almost certain.
• The insurance company uses the premia of the
lucky to pay for the unlucky.
• Using the law of large numbers can estimate the
necessary premium quite precisely.
Risk spreading
• Not all risks are independent: earthquakes, floods,
epidemics
• When risks hare highly correlated, makes it hard to
predict and hard to insure
• Many catastrophes are explicitly not covered by
insurance (”act of god”)
• But government can ’force’ insurance/solidarity.
• Taking a little of money from everybody has a
lower welfare impact then letting a few people bear
the full brunt.
• This is not a Pareto improvement! (some people
made worse off!) And hence cannot be
implemented with a market solution.
• Many of these insurance policies are implicit
• It is simply assumed that the government will help
victims of flooding, terrorist attacks, etc
• Sometimes government tries to force ex ante insurance
(e.g. compulsory flood insurance), but difficult to be
consistent when the disaster strikes.
Risk transfer
• Transfer risk from those less willing to bare it to those
more willing to bare it
• Assuming declining absolute risk aversion, a
• (p = 0.5, −$1000; p = 0.5, +$1000) bet is more
onerous on a poor individual than a rich individual.
• Thus the poor individual is willing to pay more to get
rid of the risk than the rich individual demands to
accept the risk.
• Also works with more risk averse/less risk averse in
general
Since also the low-risk types would prefer full
insurance (as long as they are risk averse) it can be
beneficial to make insurance
compulsory
If there are relatively few high-risk types, what equilibrium may have higher utility?
pooling
equilibrium may have higher utility than signaling
equilibrium.
• Advantage from full coverage may outweigh
the cost of cross-subsidization
