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Difficulty: HardLaw of Large Numbers

A regional property and casualty insurer is relying on the Law of Large Numbers to project its aggregate losses for the upcoming year across a rapidly expanding portfolio of residential homes. Which of the following statements correctly describe the application and requirements of the Law of Large Numbers in this scenario? (Select all that apply)

  1. As the number of similar residential properties in the portfolio increases, the difference between the insurer's projected aggregate losses and actual experienced losses is expected to decrease.Answer
  2. The insurer must ensure the properties added to the pool share homogeneous risk characteristics, as combining vastly disparate exposures significantly diminishes the accuracy of loss predictions.Answer
  3. C
    Because a larger risk pool increases statistical predictability, the insurer can utilize the Law of Large Numbers to safely underwrite speculative risks, such as guaranteeing the future real estate market value of the homes.
  4. D
    By relying on the Law of Large Numbers to achieve high statistical predictability, the insurer is engaging in risk avoidance rather than risk transfer.
  5. E
    To fully realize the benefits of the Law of Large Numbers, the primary insurer must cede the portfolio to a reinsurer, which subsequently transfers all direct legal liability for claims away from the primary insurer.

Answer

The correct statements are that increasing similar properties reduces the variance between projected and actual losses, and that the pool must consist of homogeneous risk characteristics.
The Law of Large Numbers operates effectively only when there is a massive volume of exposure units that share similar, or homogeneous, characteristics. As the pool of these homogeneous risks grows, the statistical variance decreases, allowing the insurer's actual aggregate losses to closely align with the expected losses calculated by actuaries.

Step-by-Step Solution

1
Analyze the core mathematical function of the Law of Large Numbers.
Identify that a larger volume of exposure units decreases the relative deviation of aggregate losses.
This confirms that the statement about actual losses approaching expected losses is correct.
2
Evaluate the underwriting prerequisites for the Law of Large Numbers.
Determine that exposure units must be independent and homogeneous.
This confirms that combining disparate exposures diminishes predictability, making the homogeneity statement correct.
3
Assess the incorrect statements against foundational insurance principles.
Identify that the Law of Large Numbers does not make speculative risks insurable, is an application of risk transfer (not avoidance), and does not alter the direct liability rules of primary insurers.
This process systematically eliminates the distractors.

Key Concept

The Law of Large Numbers requires a large volume of homogeneous exposure units to accurately predict aggregate losses, but it applies exclusively to pure risks.
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Topics

Law of Large Numbers

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