Probability as Expectation Math Example 4

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Example 4

hard
An insurance company charges \200/year for a policy. It pays \10,000 if the insured event occurs (probability 0.01) and \$0 otherwise. Calculate the insurance company's expected profit per policy.

Solution

  1. 1
    Premium collected: always \$200
  2. 2
    Expected payout: 10000 \times 0.01 + 0 \times 0.99 = \100$
  3. 3
    Expected profit per policy: 200 - 100 = \100$
  4. 4
    Over 1000 policies: expected profit = 1000 \times 100 = \100,000$ (ignoring variance in actual claims)

Answer

Expected profit = \$100 per policy. Insurance company profits in the long run.
Insurance is mathematically a positive-EV business for the insurer (and negative-EV for the customer, who buys risk reduction). Premiums are set above expected payouts to ensure profitability. This is expected value applied to real financial products.

About Probability as Expectation

Probability can be interpreted as the long-run relative frequency of an event over infinitely many identical trials of a random experiment.

Learn more about Probability as Expectation β†’

More Probability as Expectation Examples

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