Actuarially Fair Price of Insurance Policy

A Finance 4335 student asked the following question earlier today:

Q: “How do you find the actuarially fair price (premium) for an insurance policy?”

Here’s the answer I provided, which I now share with all Finance 4335 students:

A: “The actuarially fair price (premium) corresponds to the expected value of the insurance indemnity; the indemnity is the amount of coverage offered by an insurance policy. Under “full coverage”, 100% of the loss is indemnified, and in such a case, the actuarially fair premium is equal to the expected value of the loss distribution.

For what it’s worth, the concept of “actuarially fair” insurance prices/premiums, along with implications for the demand for insurance, is explained in two previously assigned readings; e.g.,

  1. on page 4 of the Supply of Insurance reading (just prior to the section entitled “Example 2: Correlated Identically Distributed Losses), the following sentence appears, “A premium that is equal to the expected outcome is called an actuarially fair premium”;
  2. on page 30 of the Basic Economics: How Individuals Deal with Risk (Doherty, Chapter 2) reading, consider the following excerpt: “Ignoring transaction costs, an insurer charging a premium equal to expected loss would break even if it held a large portfolio of such policies. This premium could be called a fair premium or an actuarially fair premium, denoting that the premium is equal to the expected value of loss (sometimes called the actuarial value of the policy). The term fair is not construed in a normative sense; rather it is simply a reference point”; and
  3. on page 43 of Doherty, Chapter 2, in the first sentence of the first full paragraph: “We know from the Bernoulli principle that a risk averter will choose to fully insure at an actuarially fair premium.””

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