Indeed, the insurance companies will charge the
same average of the probability contingent commodity,
plus a small profit for the trouble of hiring actuaries to
calculate the probability BUT the spread of the risk profiles of
the drivers must not be too large.
So, the insurance companies will charge different premiums for
different distinctively risk profile drivers eg charge different
premiums for multiple claims, drunken and dangerous
driving drivers and accident free drivers.
If due to many high risk profiles drivers and high expected
claims and as a result the average premium is charged high,
the average/low risk profile drivers will decide to opt out and the
insurance companies will make losses and decides to stop to offer
the insurance. So, there is the need to charge different premiums
for different risk profile drivers.
However, this will usually not happen as the government has made
it mandatory for all drivers to buy car insurance and so even if
the premium is very high, the drivers will still have to buy the
insurance.
In addition, there is the element of fraud and the moral hazard
of the drivers who have bought the insurance to drive less
carefully as they know that they can make claims when they met with
accidents. The insurance companies will factor in these factors too
when they charge the average premium.
Indeed, insurance companies in Singapore have been making losses
for years for offering car insurance as there are many excessive
and inflated claims and to reduce losses and make profits, the
insurance companies have required 24 hours to 48 hours
ruling for drivers to report to the insurance companies'
workshop, refuse to sell insurance to these multiple claims
drivers, raise the premium sharply not due to the fault of the
majority of the drivers but due to the excessive and inflated
claims of a minority drivers, charge different premiums for
multiple claims drivers and accident free drivers and so
on.
To factor in all these factors, we will need to formulate the
maximisation problem subject to constraints.
To summarise, insurance companies will charge a lower premium to
low risk driver and a higher premium to high risk driver.
