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Difficulty: MediumLaw of Large Numbers

A newly appointed Chief Risk Officer (CRO) at a mutual insurance company is reviewing a commercial auto portfolio that currently covers only 250 local delivery vans. The CRO notes that the year-to-year claims expenses for this group are highly erratic and unpredictable. To achieve statistically reliable and stable loss forecasts, which of the following actions directly applies the Law of Large Numbers?

  1. Writing new coverage for 15,000 additional local delivery vans operating in similar environments.Answer
  2. B
    Requiring all currently insured delivery vans to install advanced telematics and speed limiters.
  3. C
    Utilizing company surplus to purchase commodity futures, aiming to offset potential auto claims.
  4. D
    Ceding a portion of the delivery van premiums and liabilities to an established reinsurance company.

Answer

Writing new coverage for 15,000 additional local delivery vans operating in similar environments.
The Law of Large Numbers dictates that as the number of independent, homogeneous exposure units increases, the actual losses will more closely approach the expected losses. By expanding the portfolio with 15,000 similar delivery vans, the insurer gathers enough statistical data points to accurately forecast aggregate losses, thereby stabilizing their pricing and reserving models.

Step-by-Step Solution

1
Identify the core goal described in the scenario.
The Chief Risk Officer wants to achieve statistically reliable and stable loss forecasts for an erratic portfolio.
Understanding the goal helps differentiate between the statistical mechanism needed versus general risk management techniques.
2
Define the Law of Large Numbers.
The Law of Large Numbers states that as the number of independent, homogeneous (similar) exposure units increases, the statistical predictability of future losses improves.
Applying the exact definition ensures the correct strategy is selected.
3
Evaluate the options against the definition.
Increasing the number of similar vans to 15,000 directly applies this principle. The other options involve risk reduction, speculative investment, and risk transfer.
Distinguishing the Law of Large Numbers from other methods of handling risk isolates the correct answer.

Key Concept

The Law of Large Numbers mathematically improves the predictability of expected losses when a large volume of similar exposure units is pooled.
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Topics

Law of Large Numbers

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