Insurance Premiums

Probability · Axiom Academy

The mathematical foundation behind how insurance companies stay profitable You're shopping for car insurance and notice something curious: Your annual premium is 1,200, but the average accident claim is only 800. At first, this seems unfair. Why are you paying 1,200 when the expected claim is only 800? Are insurance companies just greedy? The answer lies in probability and expected value. Let's explore how insurance companies use discrete random variables to set prices that are fair for both them and their customers. Insurance companies collect vast amounts of data. Here's simplified data for young drivers (ages 22-25) over one year: Notice that the claim amount is a discrete random variable - it can only take specific values ( 0, 2,000, 8,000, or 25,000), and each outcome has a known probability. The Expected Value Calculation The expected value represents the average claim the insurance company will pay per customer over the long run: For our car insurance example: If the expected claim is 770, why doesn't the insurance company charge exactly 770 for the premium? Insurance companies charge more than the expected value for several important reasons: 1. Operating Costs (20-25%) Salaries, buildings, technology, claims processing, fraud detection, customer service 2. Risk Buffer (5-10%) Some years have more claims than expected - the company needs reserves for uncertainty 3. Profit Margin (5-10%) Investors need returns to keep the company operational and competitive

This is the written version of the interactive lesson above. See the full Probability course.