Page 35 - Insurance Times May 2023

For example, auto insurance may record and study the The more eggs we deal with, the more likely we are to find
number of accidents caused by a very large population of 18- that one out of every three-dozen is cracked.
year-old males. They will be able to predict how many 18-
Insurers use the law of large numbers to estimate the losses
year-old males will cause an accident in a given year. They a certain group of insureds may have in the future. An actuary
will know that in a given year there is a high probability that
looks at losses that have occurred in the past and predicts
X number of 18-year-old males will cause an accident.
that in the future approximately two out of 100 policyholders
Knowing this, they partially can determine how much an 18- will have a claim. Thus, if the insurers writes 100 automobile
year-old male should pay for auto insurance (excluding other policies, it may expect to pay two claims. This is referred to
factors, such as the type of vehicle, region where the driver as loss frequency.
resides, etc.) This is how the law of large numbers helps
Insurance companies must also determine the average cost
insurance providers determine their rates, and why the rates
of claims over time, or loss severity. If the average claim
vary from one type of individual to another.
resulted in the company paying Rs. 1,000, then the actuary
will predict that total losses for the upcoming year will be Rs.
Law of Large Numbers Relates to Insurance:
2,000 (two claims at Rs. 1,000 each).
(Understanding the Law of Large Numbers in
The law of large numbers states that as the number of
Insurance) policyholders increases, the more confident the insurer is its
In the insurance industry, the law of large numbers produces prediction will prove true. Therefore, insurance companies
its axiom. As the number of exposure units (policyholders) attempt to acquire a large number of similar policyholders
increases, the probability that the actual loss per exposure who all contribute to a fund which will pay the losses.
unit will equal the expected loss per exposure unit is higher.
Statistics is used to determine what risk an insured poses to
To put it in economic language, there are returns to scale in
an insurance company, what percentage of policies is likely
insurance production.
to pay out, and how much money a company can expect to
In practical terms, this means that it is easier to establish the pay out in claims.
correct premium and thereby reduce risk exposure for the
The Law of Large Numbers theorises that the average of a
insurer as more policies are issued within a given insurance
large number of results closely mirrors the expected value,
class. An insurance company is better off issuing 500 rather
and that difference narrows as more results are introduced.
than 150 fire insurance policies, assuming a stable and
In insurance, with a large number of policyholders, the actual
independent probability distribution for loss exposure.
loss per event will equal the expected loss per event.
First, all insurance companies are not equally adept at the
The Law of Large Numbers is less effective with health and fire
business of providing insurance. This includes maintaining
insurance where policyholders are independent of each other.
operational efficiency, calculating effective premiums, and
mitigating loss exposure after a claim is filed. Most of these With a large number of insurers offering different types of
coverage, the demand for variety increases, making the Law
features do not impact the law of large numbers.
of Large Numbers less beneficial.
The law of large numbers is a statistical concept that relates
to probability. It is one of the factors insurance companies
Probability Analysis in insurance:
use to determine their rates.
A technique used by risk managers for forecasting future
It means that the larger the number of units that are individually
events, such as accidental and business losses. This process
exposed to an event, the greater the likelihood that the actual
involves a review of historical loss data to calculate a
results of that exposure will equal the expected results.
probability distribution that can be used to predict future
The Law of Large Numbers using eggs as an example, that
losses. The probability analyst views past losses as a range of
for every three-dozen eggs sold by a grocer, an average of
outcomes of what might be expected for the future and
one of those eggs is cracked. Therefore, we expect that every
assumes that the environment will remain fairly stable. This
time we buy three-dozen eggs, it is likely (though not
technique is particularly effective for companies that have a
guaranteed) we will find one cracked. The more eggs we
large amount of data on past losses and that have
buy, the more likely this is. If we buy 12-dozen eggs, the
experienced stable operations. This type of analysis is
likelihood that one for every three-dozen will be cracked
contrasted to trend analysis.
increases. If we buy 18-dozen eggs, the likelihood that one
for every three-dozen will be cracked increases even more.
32 May 2023 The Insurance Times