Law of Large Numbers and Pricing Risk in Health Insurance: A Closer Look!

No one can predict the losses that a specific person or group will experience. No one knows when a specific person will need medical care. However, an insurer can predict with a fairly high degree of accuracy the number of people in a given group who will require medical care during a given period of time.

These predictions of future losses are based on the concept that, even though individual events—such as illness of a particular person—occur randomly, we can use observations of past events to determine the likelihood—or probability— that a given event will occur in the future. An important concept that helps assure us of the accuracy of our predictions about the probability of an event occurring is the Law of Large Numbers.

Insurance companies rely on the law of large numbers to help estimate the value and frequency of future claims they will pay. When it works perfectly, insurance companies run a stable business,?consumers pay a fair and accurate premium,?and the entire financial system avoids serious disruption.

What is the Law of Large Numbers?

The law of large numbers stems from the probability theory in statistics. It states that, typically, the more times we observe a particular nonrandom event, the more likely that our observed results will approximate the “true” probability that the event will occur. As the size of a sample or population increases, the average of their observed values tends to converge towards the expected value. In simpler terms, it suggests that with a larger pool of insured individuals, health insurance companies can make more accurate predictions about potential risk factors and financial outcomes.

The law of large numbers is especially important in health insurance because the cost of claims can vary widely from person to person and from group to group. Some people may never file a claim, while others may have very expensive claims. By pooling the risk of all policyholders together, insurance companies can reduce the risk of any one policyholder having to pay a high premium.

Insurance companies are able to provide protection against the financial consequences of loss because of a concept known as risk pooling. Essentially, risk pooling involves combining the contributions "premiums" of many individuals who are at risk for a potential loss in order to pay the costs for the few who actually experience the loss.

The insurer collects premiums to provide a common fund from which the insurer can pay benefits when a covered loss occurs. For the fund to be large enough to cover the insured losses, the amount a policyholder pays for each policy and contributes to the fund must be “adequate” to cover the costs of that particular risk to the insurer. Because not all individuals or groups that apply for insurance coverage present the same degree of risk to an insurer, insurance companies develop premium rate schedules for each insurance product. These premium rate schedules comprise different categories of premium rates that correspond to the various categories of risk that insured individuals or groups pose to the insurer. Insurers charge an individual or group who represents a greater risk of loss an appropriately higher premium rate for coverage.

The Power of Diverse Data

Insurance companies rely on the law of large numbers when they make predictions about the covered losses that a given group of insureds is likely to experience during a given time period. Insurance companies collect specific information, encompassing a wide range of demographics, medical histories, and other relevant information, about large numbers of people so that they can identify the pattern of losses that those people experienced.

Improved Predictability and Accuracy

Thanks to this statistical principle, health insurance companies can make informed decisions about coverage options, benefits, and pricing structures. This enhances their ability to accurately forecast future claims, manage reserves, and maintain a financially sound operation.

The accuracy of the prediction of future losses is lower for smaller groups. Large groups tend to more closely follow actuarial predictions of morbidity. They also have fewer and smaller fluctuations in claims. In general, the smaller the group, the less likely the group’s claim experience will approximate its expected claim experience.

Managing Risk and Premiums

Health insurance companies use the law of large numbers to set premiums and predict future claims. Insurers request medical claims experience to price a risk because it helps them to better understand the expected loss experience for that risk. By having data on the medical claims history of a group, insurers can get a good sense of how many people in the group are likely to file claims "frequency", and how much those claims will cost "severity".

This information is essential for insurers to set premiums accurately. If insurers set premiums that are too low, they may not be able to cover the cost of claims, which could lead to financial losses. If insurers set premiums that are too high, they may lose customers to competitors who offer lower premiums.

The law of large numbers helps insurers to set premiums accurately by allowing them to pool the risk of all policyholders together. This reduces the risk for any one policyholder of having to pay a high premium.

Refining Risk Assessment

The law of large numbers empowers insurers to refine their risk assessment processes by incorporating more comprehensive and representative data. By examining claims experience from a significant number of policyholders, insurers can better understand the health risks and cost patterns within a specific demographic or group. This enables them to make more accurate predictions and adjustments when pricing risks.

Balancing Risk and Affordability

The accuracy of risk assessment is vital for insurers to strike a balance between managing risk and making insurance coverage affordable. By leveraging the law of large numbers and analyzing claims experience, insurers can ensure that premiums adequately reflect the expected costs associated with providing coverage, while still remaining affordable for policyholders.

Balancing Growth and Profitability

The law of large numbers allows insurers to grow their businesses without sacrificing profitability.

The more policyholders an insurer has, the more accurate its predictions of future claims will be. This allows the insurer to set premiums that are high enough to cover the cost of claims, plus a profit margin, without having to charge excessively high premiums to individual policyholders.

For example, if an insurer has only 100 policyholders, it may be difficult to predict how many claims it will have to pay in a given year. As a result, the insurer may have to charge higher premiums to account for the uncertainty.

However, if an insurer has 100,000 policyholders, it will be much better able to predict how many claims it will have to pay. This allows the insurer to set lower premiums, while still maintaining a profit.

Mitigating Adverse Selection

Adverse selection occurs when individuals with higher risks are more likely to seek insurance coverage. However, the law of large numbers helps mitigate this by allowing insurers to pool a large number of individuals together. By having a diverse mix of policyholders, insurers can balance the risks and prevent adverse selection, ensuring that their customer base remains sustainable and profitable.

Promoting Stability and Sustainability

By utilizing the law of large numbers, insurers can spread the risk across a large pool of policyholders. This helps to stabilize the financial impact of high-cost claims, ensuring that the overall system remains sustainable and affordable for everyone involved.

Identifying fraud

Insurance companies can use the law of large numbers to identify patterns that may indicate fraud. For example, if a company notices that a certain group of policyholders is filing a higher-than-average number of claims, it may investigate to see if there is any fraud occurring.

Embracing Technological Advancements

In today's digital era, technological advancements are accelerating the potential of the law of large numbers. AI algorithms, machine learning, and big data analytics are transforming the way insurers analyze and interpret vast amounts of health-related data, further enhancing their risk assessment capabilities.

The law of large numbers is a powerful tool that helps health insurers operate efficiently and provide affordable coverage to their policyholders. As we move forward, the law of large numbers will continue to shape the landscape of health insurance, enabling insurers to provide comprehensive coverage, manage risks, and improve the overall well-being of individuals and communities.