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 of the insurer. The expected payout is calculated by multiplying the probability of each event by its corresponding payout and summing these values up. An actuarially fair premium equals the expected payout without including any profit margin or administrative costs. For example, if a homeowner wants to buy insurance against natural disasters with a payout of $50,000 and a 1% probability of damage, the actuarially fair premium for this policy would be \( 0.01 * 50,000 = $500 \).

Step-by-step solution

Define Expected Payout

Expected payout refers to the average amount the insurer will pay to the policyholder, considering the probability of payouts for various events covered by the insurance policy. It is calculated by multiplying the probability of each event by its corresponding payout and summing these values up.\( \text{Expected Payout} = \sum_{i=1}^{n}(P_i * Payout_i) \), where \( P_i \) represents the probability of event i occurring, and \( Payout_i \) denotes the payout for event i.

Define Premium

A premium is the amount the policyholder pays for an insurance policy. The insurer calculates this amount by considering various factors, such as the expected payout, administrative costs, and profit margin.

Determine Actuarially Fair Premium

An actuarially fair premium is the premium that equals the expected payout. In other words, the insurer charges the exact amount it is expected to pay to the policyholder, without including any profit margin or administrative costs.

Example

Suppose a homeowner wants to buy insurance against their house getting damaged due to a natural disaster. The insurance policy pays out $50,000 if the house is damaged. Based on historical data, the probability of the house getting damaged is 1%. To calculate the actuarially fair premium for this insurance policy, we would use the following formula: \( \text{Actuarially Fair Premium} = \text{Expected Payout} \) In this case, there is only one possible event to consider: the house gets damaged with a 1% probability. Thus, the expected payout is: \( \text{Expected Payout} = P1 * Payout1 = 0.01 * \(50,000 = \)500 \) Therefore, an actuarially fair insurance premium for this policy would be $500.