Insurance mathematics is the area of applied mathematics that studies different risks to individuals, property and businesses, and ways to manage these risks. Insurance mathematics relies heavily on calculus, probability, statistics and interest theory. These disciplines are used in insurance to interpret data from past events, and to model future events. Some applications of insurance mathematics are pricing insurance policies, determining cash reserves to cover claims incurred, and modeling capital asset allocation scenarios.
Insurance mathematics is one of the many tools used in actuarial science to assess risk. By definition, a risk is the possibility of the occurrence of a hazard. Individuals are exposed to risks such as sickness, disability and death. Property could be stolen, destroyed in a fire or by a flood. Businesses could be interrupted by natural disasters or suffer losses from lawsuits.
Insurance mathematics is used to better define and manage these risks. Life insurance protects individuals and other insurance protects property and businesses, reducing the financial impact of unforeseen events. Risk theory is used to define the likelihood that a hazard will actually occur, and to measure the financial impact of the hazard.
Insurance mathematics draws upon many sub fields of mathematics. Calculus is the foundation of most insurance mathematics. Probability is another fundamental subject when defining the uncertainty of hazards. Statistics is important in order to study past events. Interest theory and other financial mathematical topics are important when defining the present value of future payments.
In order to better predict the future, the past is studied and combined with good judgement in order to model risks. Statistical methods, such as regression and time series models, are used to extract useful information from historical data. This information is used to create models to predict future occurrences. Some frequently used models are survival models, markov chain models, frequency and severity models, aggregate models, empirical models and parametric models.
Once insurance mathematics has been used to model future events, this model can be applied to the insurance business. The expected number and severity of claims can be used to price insurance policies. The model can also be used to determine how much cash will be necessary to cover future claims and expenses. Models are used to analyze corporate financing scenarios which often contain derivatives, in order to hedge different types of asset risk. Using theory or simulation, different investment strategies are studied, requiring an intimate knowledge of financial mathematics.