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journal article Risk, Insurance, and SamplingThe Journal of Risk and Insurance Vol. 31, No. 4 (Dec., 1964) , pp. 511-538 (28 pages) Published By: American Risk and Insurance Association https://doi.org/10.2307/250806 https://www.jstor.org/stable/250806 Read and download Log in through your school or library Alternate access options For independent researchers Read Online Read 100 articles/month free Subscribe to JPASS Unlimited reading + 10 downloads Purchase article $9.00 - Download now and later Journal Information The Journal of Risk and Insurance publishes rigorous, original research in insurance economics and risk management. This includes the following areas of specialization: (1) industrial organization of insurance markets; (2) management of risks in the private and public sectors; (3) insurance finance, financial pricing, financial management; (4) economics of employee benefits, pension plans, and social insurance; (5) utility theory, demand for insurance, moral hazard, and adverse selection; (6) insurance regulation; (7) actuarial and statistical methodology; and (8) economics of insurance institutions. Both theoretical and empirical submissions are encouraged. Empirical work should provide tests of hypotheses based on sound theoretical foundations. JSTOR provides a digital archive of the print version of The Journal of Risk and Insurance. The electronic version of The Journal of Risk and Insurance is available at http://www.blackwell-synergy.com/servlet/useragent?func=showIssues&code;=jori. Authorized users may be able to access the full text articles at this site. Publisher Information The American Risk and Insurance Association (ARIA) is a worldwide group of academic, professional, and regulatory leaders in insurance, risk management, and related areas, joined together to advance the study and understanding of the field. Founded in 1932, ARIA emphasizes research relevant to the operational concerns and functions of insurance and risk management professionals and provides resources, information, and support on important insurance and risk management issues. Two main goals of the organization are 1) to expand and improve academic instruction of risk management and insurance, and, 2) to encourage research on all significant aspects of risk management and insurance. Rights & Usage This item is part of a JSTOR Collection.
Insurance companies rely on the law of large numbers to help estimate the value and frequency of future claims they will pay to policyholders. 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. However, the theoretical benefits from the law of large numbers do not always hold up in the real world. Key Takeaways
Watch Now: What Is the Law of Large Numbers?What is the Law of Large Numbers?The law of large numbers stems from the probability theory in statistics. It proposes that when the sample of observations increases, variation around the mean observation declines. In other words, the average value gains predictive power. For example, consider a simple trial in which someone flips a quarter. Every time the quarter lands on heads, the person records one point. No points are recorded when it lands as tails. The expected value of a coin flip in this trial is 0.5 points because there is only a 50% chance that the quarter will land as heads. If you only flip the coin twice, the average value could end up far from the expected value. Consecutive heads produce an average value of one point while two tails have an average value of zero points. Increasing the number of observations is more likely to yield an average value closer to the expected value. If there are 53 heads and 47 tails during 100 flips, the average value would be 0.53, which is very close to the 0.5 expected value. This is how the law of large numbers works. Understanding the Law of Large Numbers in InsuranceIn the insurance industry, the law of large numbers produces its axiom. As the number of exposure units (policyholders) increases, the probability that the actual loss per exposure unit will equal the expected loss per exposure unit is higher. To put it in economic language, there are returns to scale in insurance production. In practical terms, this means that it is easier to establish the correct premium and thereby reduce risk exposure for the insurer as more policies are issued within a given insurance class. An insurance company is better off issuing 500 rather than 150 fire insurance policies, assuming a stable and independent probability distribution for loss exposure. To see it another way, suppose that a health insurance company discovers that five out of 150 people will suffer a serious and expensive injury during a given year. If the company insures only 10 or 25 people, it faces far greater risks than if it can ensure all 150 people. The company can be more confident that 150 policyholders will collectively pay sufficient premiums to cover the claims from five customers who suffer serious injuries. Special ConsiderationsThere were nearly 5,965 insurance carriers in the United States as of 2019, according to the National Association of Insurance Commissioners. Some carriers are more successful than others who provide the same or similar types of coverage. If there are increasing returns to scale in insurance, thanks to the law of large numbers, then why are there so many insurance companies rather than a few giants dominating the industry? First, all insurance companies are not equally adept at the business of providing insurance. This includes maintaining operational efficiency, calculating effective premiums, and mitigating loss exposure after a claim is filed. Most of these features do not impact the law of large numbers. However, the law of large numbers becomes less effective when risk-bearing policyholders are independent of one another. This is most easily seen in the health and fire insurance industries because diseases and fire can spread from one policyholder to another if not properly contained. This problem is known as contagion. There are also potentially insurable risks for which the law of large numbers theoretically could be useful, but there are not enough potential customers to make it work. Consider trying to insure a city against the risk of nuclear or biological warfare. It would take thousands or millions of major cities paying premiums to offset the cost of one realized risk. There aren't enough cities in the world to make it work. Finally, each insurance consumer has an individual risk preference, time preference, and price point for insurance. As the variety in demands increases, the potential benefit from the law of large numbers decreases because fewer people want similar types of coverage. Which one of the following describes the effect underwriting standards can have on premium?Which one of the following describes the effect underwriting standards can have on premium? A. If more causes of loss are covered, premiums will increase.
How do insurance companies determine risk exposure?The level of exposure is usually calculated by multiplying the probability of a risk incident occurring by the amount of its potential losses. Risk exposure in business is often used to rank the probability of different types of losses and to determine which losses are acceptable or unacceptable.
What are exposures in insurance?Exposures are a measure of what is being insured. For example, an insured vehicle is an exposure. The term earned means that the exposures were in fact at risk of a loss in the period in question.
Which one of the following items is a responsibility of the underwriting management of an insurance company?One of the responsibilities of underwriting management is to arrange reinsurance. One type of reinsurance is arranged to automatically reinsurance a portion of all eligible risks of the primary insurer.
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Which one of the following is the fundamental measure of loss exposure used in insurance rating?
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