Page 41 - Insurance Times June 2023

However, insurance uses only the more restricted definition Insurance companies must take into account many more than
of economic loss, since only economic losses are insurable two outcomes, as life is not as simple as a 50/50 coin toss.
risks. Hence, in insurance, a loss is the unexpected reduction However, they use the same basic formula to determine how
in the economic value of one's possessions. Insurance much they are likely to pay out to sets of policyholders who
companies use this definition because they can only cover have the same type of policy. This result gives them an idea of
such a loss with the payment of money. A loss differs from an how much money they need to collect to cover their potential
expense, which is an expected payment for a good or service. losses (the amount they pay out).
Thus, buying gas for your car is an expense, while a car
accident is a loss. Going back to the coin example, on the first two flips, the 50/
50 split that one would expect with a 50% probability may
Chance of loss is the probability that a loss will occur, which not occur and it may land on heads twice, then tails, then
can either be an expected loss or an actual loss, divided by heads again. This makes the probability of getting one
the number exposed to loss, or the sample population. outcome less predictable. This is where the law of large
numbers comes in. The law of large numbers states that the
Expected or Actual Loss more data points there are, the more accurate an outcome
Chance of Loss =
prediction will be. Continuing to flip the coin and record the
Number of Possible Losses
results (say, 100 times or more), the probability will become
closer to 50%.
Because the chance of loss is only an average, actual losses
may differ significantly from expected losses, especially for
Pricing mechanism of insurance:
small samples, but as the sample size increases, actual and
expected losses tend to converge. Pricing is one of the most essential components of an insurance
company. It is the process by which an insurance company
sets up the premium that needs to be charged from
Probabilities of insurance claim:
policyholder by considering various risk factors such as age,
For an individual, the probability of having an accident in a
mortality, gender, location, etc. These are some of many
period of 24 hrs (and therefore the probability of making a
factors used by the insurance sector for calculating premium
claim) is 0.00037. Claims on successive days are independent,
and will vary with the nature of the product being priced. It is
and a person cannot have more than two accidents in one
one of the task of an Actuary to perform pricing in General
day.
Insurance company.
What is the premium should the insurer charge for each or
To calculate the premium amount, a very important concept
policy to assure or ensure that the premium income will cover
is used called the "Generalised Linear Models" which is used
the cost of all the claims.
by the Pricing team for a really precise premium calculation
since it can accommodate many factors. As more factors are
A car insurance company has 2,500 policy holder and the
added, more accuracy will be there in premium calculation
expected claim paid to a policy holder during a year is 1,000
but one should remember that every additional factor should
with a standard deviation of 900
have a significant effect in terms of explaining the variability
of the dependent variable, which in this case will be the
What premium should the company charge each policy holder
premium to be charged. The significant effect for each added
to assure that with probability 0.999 the premium income
factor is important because each additional factor is
will cover the cost of the claims.
associated with heavy cost in terms of modelling time and
analysis which the insurance company has to bear.
And we need to look at the aggregate claims random
variable. The idea is that the insurer needs to collect sufficient
In this highly competitive world, if one has to survive in the
premiums to cover the aggregate claims with at least 0.999
market it is important to keep the price of products
probability.
competitive to what other companies are charging. And to
do so, premium is charged lowered than the actual calculated
Simple probability is the calculation of an outcome or the
one which leads underwriting losses also and that is why,
chance of an event ever happening. Insurance companies
pricing in General Insurance requires an Actuary to focus on
use probability statistics to determine the chances of having
each and every aspect of the product being made.
to pay out a claim.
The Insurance Times June 2023 37