Mathematician

===Consulting===
Many careers in mathematics outside of universities involve consulting. For instance, actuaries assemble and analyze data to estimate the probability and likely cost of the occurrence of an event such as death, sickness, injury, disability, or loss of property. Actuaries also address financial questions, including those involving the level of pension contributions required to produce a certain retirement income and the way in which a company should invest resources to maximize its return on investments in light of potential risk. Using their broad knowledge, actuaries help design and price insurance policies, pension plans, and other financial strategies in a manner which will help ensure that the plans are maintained on a sound financial basis.

As another example, mathematical finance will derive and extend the [[Mathematical model|mathematical]] or [[Numerical analysis|numerical]] models without necessarily establishing a link to financial theory, taking observed market prices as input. Mathematical consistency is required, not compatibility with economic theory. Thus, for example, while a financial economist might study the structural reasons why a company may have a certain [[share price]], a financial mathematician may take the share price as a given, and attempt to use [[stochastic calculus]] to obtain the corresponding value of [[Derivative (finance)|derivative]]s of the [[stock]] (''see: [[Valuation of options]]; [[Financial modeling#Quantitative finance|Financial modeling]]'').