Premium Construction: The Cost of Risk and Management

The monthly premiums we pay are not just a simple division of the expected insurance payouts. A premium is a sum of several precisely calculated components.

1. The Equivalence Principle

This is the most fundamental principle in actuarial science. It states that: “The present value of total premium income must equal the present value of total expected benefit payouts and expenses.” Keeping this mathematical balance ensures the company’s stability.

2. The Structure of a Premium

The total premium (Gross Premium) is broadly divided into the Net Premium and the Loading.

• Net Premium: The portion meant to fund future benefit payouts (composed of Risk Premium + Savings Premium).
• Loading (Expense Premium): The portion used to cover the insurance company’s operating costs (acquisition, maintenance, and collection costs).

3. The Three Factor Model

There are three critical variables that determine the size of a premium:

1. Assumed Mortality: How many people are expected to suffer a loss?
2. Assumed Interest Rate: How much can we earn by investing the premiums?
3. Assumed Expense Ratio: How much will it cost to run the company?

💡 Professor’s Tip

When the assumed interest rate increases, the premium paid by the customer decreases. This is because if the company can earn more through investments, it needs to collect less from customers. Conversely, in a low-interest environment, premiums face upward pressure.

🔗 Next Step

• Ch5: Insurance Reserves