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Difficulty: HardLaw of Large Numbers

A financial institution introduces a new insurance policy designed to protect venture capitalists against the loss of capital if their funded tech startups fail to reach profitability. The chief product actuary argues that by aggressively marketing the policy and aggregating over 100,000 independent startup exposures globally, the Law of Large Numbers will mathematically guarantee accurate aggregate loss predictions and stabilize premium rates. According to fundamental insurance principles, why is the actuary's reliance on the Law of Large Numbers flawed in this specific scenario?

  1. A
    The insurer is incorrectly attempting to utilize risk transfer for an exposure that the Law of Large Numbers dictates must be handled through risk retention.
  2. B
    The financial failure of a startup constitutes a hazard rather than a discrete peril, which prevents the mathematical formulas of the Law of Large Numbers from applying.
  3. The Law of Large Numbers accurately predicts aggregate losses only for pure risks, whereas startup profitability represents an uninsurable speculative risk.Answer
  4. D
    The statistical predictability of the Law of Large Numbers cannot be achieved unless the primary insurer acts as a ceding company and transfers the excess liability to a reinsurer.

Answer

The Law of Large Numbers accurately predicts aggregate losses only for pure risks, whereas startup profitability represents an uninsurable speculative risk.
The correct answer accurately synthesizes two foundational concepts: the requirement of pure risk and the mechanics of the Law of Large Numbers. The Law of Large Numbers allows insurers to predict aggregate losses when they have a large volume of homogeneous exposures. However, this mathematical principle is entirely contingent on the exposures being insurable in the first place. Startup investments involve a chance of financial gain, making them speculative risks. Because speculative risks are fundamentally uninsurable, aggregating 100,000 of them does not validate the use of the Law of Large Numbers for premium stabilization.

Step-by-Step Solution

1
Analyze the nature of the risk described in the scenario (investing in tech startups).
The risk involves the potential to lose invested capital, but also inherently involves the potential to make a profit.
Identifying whether a risk is pure or speculative is the first step in determining insurability.
2
Classify the risk based on fundamental insurance definitions.
Because the risk involves a chance of financial gain as well as loss, it is classified as a speculative risk.
Pure risk involves only the chance of loss or no loss, whereas speculative risk involves the chance of gain, loss, or no change.
3
Evaluate the actuary's application of the Law of Large Numbers to this classification.
The actuary assumes that aggregating 100,000 policies makes the risk predictable and therefore insurable.
The Law of Large Numbers requires a large number of exposure units to predict aggregate losses accurately.
4
Identify the foundational flaw in the actuary's reasoning.
The Law of Large Numbers can only be applied to pure risks. Aggregating uninsurable speculative risks does not magically make them insurable.
For the mathematical principle of the Law of Large Numbers to work in insurance pricing, the underlying exposures must meet the basic elements of an insurable risk, the most critical being that it must be a pure risk.

Key Concept

The Law of Large Numbers and Prerequisites for Insurable Risk
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Topics

Law of Large Numbers

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