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Insurance plays an very important role in modern society, with insurance products used by everyone from large business enterprises right down to individual people and families. There are a number of mathematical equations and models which are essential to the inner workings of the insurance industry, and applied to all areas of risk management, premium determination, and the principles of pricing and hedging. Every type of insurance; including life insurance, health insurance, car insurance (insurance64.co.uk), home insurance, and property insurance depends on the mathematical application of data to ensure an accurate and representational measurement of both premiums and risk.

There are a number of different fields of mathematics used in these applications, including such diverse areas as Markov chain models, differential equations, statistics, probability, and a number of other principles of applied mathematics. Insurance mathematics is also known as actuarial science, the discipline directly involved in the application of statistical measurements in order to assess risk. While actuarial science is a multi-disciplinary field that also involves the subjects of finance, economics, and computer programming, there is a strong probability-based mathematical basis to most of its applications. Actuaries are the professionals who are directly involved in this field, and in a number of countries around the world they must pass rigorous professional examinations in order to qualify for their profession.

The majority of actuarial methodologies are concerned with the notion of risk management, as this is one of the influential factors that effects how insurance firms price individual insurance policies. Some of the mathematical applications that play a role in these measurements include the estimating of future contingent events, discounting the value of invested funds, and measuring the probability of risk associated with various policy types. Every type of insurance is different in regard to the diversity of risk and how it measures this risk, and many actuaries specialise in particular areas of the insurance industry. For example, the risks associated with a health insurance contract are very different to those associated with a life insurance policy, and different mathematical models may be needed to come to a measured evaluation of risk and pricing. Mathematics plays a very important role in the insurance industry, and the application of specific mathematical techniques are essential to the way risk is defined and measured across the entire field of insurance.