## The Anatomy of Insurance: The Actuarial Lens (Part 2)

Written by: Leo ,

December 14, 2018*” Risk pooling is what makes insurance successful. By pooling the risk of policyholders, insurance companies can redistribute individual losses across its members.” – *Leo

Many of us look for economic security and stability. An individual with economic security is able to satisfy his essential needs of food, water, shelter and medical care, in the present and in the future. However, there’s a probability of losing that economic security from an unexpected event. Economic risk is the possibility of losing economic security. Most economic risk derives from variation from the expected outcome.

Modern society provides many examples of risk. A homeowner faces the possibility of an economic loss caused by a house fire. A driver faces a potential economic loss if his car is damaged. A larger possible economic risk exists, with respect to potential damages a driver might have to pay, if he injures a third party in a car accident for which he is responsible.

Historically, economic risk was managed through informal agreements within a defined community. For instance, if a farm was totally burnt and a herd of milking cows was destroyed, the community would pitch in to rebuild the farm and to provide the farmer with enough cows to replenish the milking stock. This cooperative (pooling) concept became formalized in the insurance industry. Under a formal insurance arrangement, each insurance policy purchaser (policyholder) still implicitly pools his risk with all other policyholders. However, it is no longer necessary for any individual policyholder to know or have any direct connection with any other policyholder

The essence of insurance entails incurring a small cost in the form of *premium* to obtain protection against an event that could potentially cause significant financial losses. In most cases, by paying a small premium, we can eliminate the possibility of paying large amounts of money when things go awry. Insurance is usually provided by insurance companies that pool the risk of many policyholders. The law of large numbers enables insurance companies to fairly observe and predict how much money is needed to accommodate all the claims in their pool, without threatening its financial health.

“Risk pooling; the entire pool compensates the unfortunate few”

From an actuarial lens, insurance companies consider the losses expected for the insurance pool and the potential for variation in order to charge premiums that, in total, will be sufficient to cover all of the projected claim payments for the insurance pool. The larger the policy pool, the more predictable the results will be. Normally, only a small percentage of policyholders suffer losses. Their losses are paid out of the premiums collected from the pool of policyholders. Thus, the entire pool compensates the unfortunate few. Each policyholder barters an unknown loss for the payment of a known premium.

Losses depend on two random variables. The first is the number of losses that will occur in a specified period. For example, a young and healthy policyholder with hospital insurance will have no losses in most years, but in some years he could have one or more accidents or illnesses requiring hospitalization. This random variable for the number of losses is commonly referred to as the frequency of loss and its probability distribution is called the frequency distribution. The second random variable is the amount of the loss, given that a loss has occurred. For example, the hospital charges for an overnight hospital stay would be much lower than the charges for an extended hospitalization. The amount of loss is often referred to as the severity and the probability distribution for the amount of loss is called the severity distribution. By combining the frequency distribution with the severity distribution we can determine the overall loss distribution.

Example: Consider a car owner who has an 80% chance of no accidents in a year, a 20% chance of being in a single accident in a year, and no chance of being in more than one accident in a year. For simplicity, assume that there is a 50% probability that after the accident the car will need repairs costing $500, a 40% probability that the repairs will cost $5000, and a 10% probability that the car will need to be replaced, which will cost $15,000. Combining the frequency and severity distributions forms the following distribution of the random variable X, loss due to accident:

On average, the car owner spends 750 on repairs due to car accidents. A 750 loss may not seem like much to the car owner, but the possibility of a 5000 or 15,000 loss could create real concern.

Understanding the actuarial aspect of insurance can help us have a broader view of how insurance premium is derived. We can then evaluate the premiums we pay, in a way that it rationally justifies the the insurance payout with relevance to the probability of an insured event happening. For example, some of us buy a Critical Illness (CI) insurance policy so that in the probable event of contracting a CI, such as Cancer (1 in 3 people will develop cancer in their lifetime), we can receive a lump sum payout. We can choose to exercise the option of spending the money on necessary cancer treatment or to fund family financial commitments (child’s education, utility expenses, etc).

“Actuaries are the cool kids of the insurance world”

At the most basic level, actuaries possess the mathematical, statistical and business skills needed to determine the expected costs and risks in any situation where there is financial uncertainty and sufficient data for creating a model of those risks. For insurance, this includes developing net premiums (benefit premiums), gross premiums, and the amount of assets the insurer should have on hand to assure that benefits and expenses can be paid as they arise.

The actuary would begin by trying to estimate the frequency and severity distribution for a particular insurance pool. This process usually begins with an analysis of past experience. The actuary will try to use data gathered from the insurance pool or from a group as similar to the insurance pool as possible. For instance, if a group of active workers were being insured for healthcare expenditures, the actuary would not want to use data that included disabled or retired individuals.

Since insurance business exists to protect against the financial consequences of adverse events, it is not surprising that actuaries are involved in many aspects of the operations of insurers. The actuarial control cycle highlights the areas in which actuaries can contribute to the financial well-being of an insurer. With good financial health, insurance companies can assure that benefits and payouts will be handed to policyholders as they arise.

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