fundamental insurance equation

Imagine you run a small insurance company and you have to decide what to charge a customer for a year of coverage. You cannot just guess. The money you collect has to do four jobs: pay the claims that will happen, pay your costs of running the business, leave a little for a fair profit, and (with luck) not be wildly too high or too low. The fundamental insurance equation is just the plain statement of that balance.

In words it says: Premium = Losses + Loss Adjustment Expense + Other Expenses + Profit. The 'losses' are the claims you expect to pay; loss adjustment expense is the cost of investigating and settling those claims; other expenses are things like commissions, taxes, and overhead; profit (often called the underwriting profit and contingencies provision) is the reward for putting capital at risk. For example, if you expect to pay 600 dollars of losses per policy, 60 dollars to handle claims, 90 dollars of general expenses, and want 50 dollars of profit, the indicated premium is 800 dollars. Crucially, every quantity on the right is a forecast of the future policy period, not a record of the past.

This one line is the backbone of almost all property-casualty pricing. Every technique you will meet — trending losses, developing losses to ultimate, on-leveling premium, picking a permissible loss ratio — exists to estimate one piece of this equation as accurately as possible for the period the rates will be in force. Get any term badly wrong and the whole price is wrong: too high and customers leave, too low and the company slowly goes broke.