Question

Insurance companies collect annual payments from homeowners in exchange for paying to rebuild houses that burn down. a) Why should you be reluctant to accept a \(\$ 300\) payment from your neighbor to replace his house should it burn down during the coming year? b) Why can the insurance company make that offer?

Short answer

Individuals face unsustainable risk, while companies spread risk among many clients.

Step-by-step solution

Understanding the Scenario

The scenario describes a common insurance practice where a homeowner pays an annual fee to an insurance company, which in turn agrees to cover the cost of rebuilding the house if it burns down.

Analyzing the Risks for Individual

If you personally accept a $300 payment to insure your neighbor's house, you take on the risk of having to pay an enormous sum potentially running into hundreds of thousands of dollars if their house burns down. This is financially unsustainable for an individual.

Considering the Insurance Company Model

Insurance companies pool risks across many clients. By having a large number of policyholders, the company can statistically predict and manage the risks of payouts. The premiums collected from all customers should cover the potential claims due to the law of large numbers.

Key concepts

Risk Management

Insurance is fundamentally about managing risk. When an individual offers to insure their neighbor's home for just $300, they take on a massive risk. If the house were to burn down, they would need to have resources, potentially hundreds of thousands of dollars, to cover the cost of rebuilding. This is not a smart approach to risk management, as the financial burden is overwhelmingly high for a single individual.

Insurance companies, however, are experts in risk management. They collect premiums from many policyholders, which helps spread the risk. They use these premiums to pay for claims and manage the uncertainty of payouts.

This risk pooling ensures the sustainability and stability of insurance services. Moreover, insurance firms also employ actuaries to assess and analyze risk probabilities, helping them set appropriate premium rates that safeguard their business and fulfill obligations.

Law of Large Numbers

The law of large numbers is a crucial principle underpinning insurance. This statistical concept states that as a sample size becomes larger, the sample mean will get closer to the expected value.

For insurance companies, this translates to predictability in outcomes. By insuring large numbers of houses, they can more accurately estimate the probability of claims and determine adequate premiums to cover these claims.

For example, while it's hard for one person to predict if a single house will burn down, it's more certain that a few houses out of thousands will. This predictability helps insurers plan effectively and ensures they have enough funds to cover the payouts without risking bankruptcy.

By relying on the law of large numbers, insurance firms can provide services that would be too risky or costly for individuals alone.

Financial Sustainability

For insurers, financial sustainability means balancing income from premiums with potential payouts for claims. This is a complex balancing act achievable through actuarial science, risk pooling, and adherence to regulatory requirements.

First, they assess the risk levels associated with different clients and adjust their premiums accordingly. This ensures fairness and profitability.

Second, by having a wide pool of insured clients, they mitigate the risk of a significant number of claims occurring simultaneously. This diversification of risk is key to financial sustainability, allowing companies to cater to claims as they arise without jeopardizing their financial health.

And finally, insurance companies set aside reserves for claims and work within strict regulatory frameworks to ensure they remain solvent, protecting their customers' interests while maintaining business viability.