Question

What is an actuarially fair insurance policy?

Short answer

An actuarially fair insurance policy is one where the premium paid by the policyholder is equal to the expected payout from the insurance company. Mathematically, this can be represented as: \(P = p \times A\), where \(P\) is the insurance premium, \(p\) is the probability of the insured event happening, and \(A\) is the payout amount in case the event occurs.

Step-by-step solution

Define the terms

Insurance premium (P): The amount paid by the policyholder to the insurance company for coverage. Expected payout (E): The anticipated amount that the insurance company will pay the policyholder, calculated by the formula E = Probability (p) × Payout amount (A).

Describe an actuarially fair insurance policy

An actuarially fair insurance policy is one where the premium paid by the policyholder is equal to the expected payout from the insurance company. Mathematically, this can be represented as: \(P = E\) or \(P = p \times A\)

Calculate the premium for an actuarially fair insurance policy

To find the premium for an actuarially fair insurance policy, we can use the formula from step 2: \(P = p \times A\) Here, \(p\) represents the probability of the insured event happening, and \(A\) represents the payout amount in case the event occurs. The product of these two values will give us the actuarially fair insurance premium.