What mathematical approaches do actuaries primarily use?

Actuaries primarily use statistics and economic modeling because these tools allow them to analyze and interpret data related to insurance risk and financial outcomes. Statistics provides actuaries with the methodologies needed to collect, review, and interpret quantitative data effectively, which is crucial for predicting future financial events and making informed decisions about insurance policies and pricing. Economic modeling complements this by enabling actuaries to simulate various economic scenarios and assess their potential impacts on insurance products. Together, these approaches help actuaries to evaluate risks, set premiums, and ensure that insurers remain financially viable while fulfilling their obligations to policyholders.

Other approaches like logic and reasoning or qualitative analysis play supporting roles but do not embody the primary mathematical techniques actuaries rely upon in their core work. Randomized testing methods, while useful in certain contexts, are not a mainstay of actuarial practice as they are more common in scientific research and experimental design rather than in the applied financial field of actuarial science.