Insurance is a tool used for risk treatment. It is dealing with many sciences and human activities. Actuarial science, which itself is based on statistics, mathematics and economics carries out technical calculations for insurance. In this paper, we first review the main roles of actuarial science in the area of insurance and then discuss the role of reliability theory for this purpose. Further, considering individual and collective risk models, we talk about the usefulness of the stochastic ordering in insurance. Finally, we discuss several questions using the current stochastic ordering literature in insurance.
