The property and casualty (P&C) insurance industry is a vital component of the global economy, providing financial protection to individuals and businesses against unforeseen events such as natural disasters, accidents, and lawsuits. Two critical components of P&C insurance are ratemaking and loss reserving, which are essential for ensuring the financial stability and sustainability of insurance companies. In this article, we will provide an introduction to ratemaking and loss reserving for property and casualty insurance.

Ratemaking is the process of determining the premium rates that insurance companies charge their policyholders for coverage. The goal of ratemaking is to set premiums that are fair, competitive, and sufficient to cover the expected losses and expenses of the insurance company. Ratemaking involves analyzing historical data, industry trends, and other factors to estimate the frequency and severity of future losses.

Pure Premium=Incurred LossesNumber of Exposure UnitsPure Premium equals the fraction with numerator Incurred Losses and denominator Number of Exposure Units end-fraction

The BF method blends an a priori expected loss ratio with the observed development. It is more stable than CL for immature accident years or volatile lines (e.g., catastrophe-prone property). Formula: [ \textUltimate Loss = \textExpected Loss \times (1 - \textExpected % Reported) + \textPaid Loss ]

An insurance premium must cover multiple financial components. It is mathematically summarized as:

Reserving is the process of estimating the amount of money an insurer must set aside to pay for claims that have already happened. These liabilities appear on the balance sheet as (or Loss and Loss Adjustment Expense Reserves).

The premium must cover both fixed and variable expenses.

| Function | Core Question | Time Focus | Key Stakeholder | | :--- | :--- | :--- | :--- | | | "What premium should we charge today for a policy that starts now?" | Prospective (Future) | Underwriting, Sales, Product Mgmt | | Loss Reserving | "How much money must we hold today for claims already happened?" | Retrospective (Past) | Finance, Claims, Actuarial, Regulators |

Property and Casualty (P&C) insurance operates on a unique economic model where the price (premium) is set before the cost of goods sold (losses) is known. This paper introduces the two core actuarial functions that manage this uncertainty: ratemaking (prospective pricing) and loss reserving (retrospective liability estimation). We explore the foundational principles, key methodologies (including the Loss Ratio, Pure Premium, and Chain Ladder methods), and the regulatory and financial reporting contexts (GAAP, SAP, IFRS 17) that govern these practices.

Estimating claims that have happened but haven’t been filed yet.

Claims that have occurred but have not yet been reported to the carrier.