risk comparison using stochastic ordering

Risk is a vital concept for many scinces like as actuarial science. actuaries, start with identifying risks, analyzing risks and then prioritize risks. these steps called risk assessment which constitute the main cor of risk management. as it comes from the name and definition of risk, it is assosiated with randomness. so, risk assessment needs statistical perspective. particularely, we need powerful techniques to compare random variables, random vectors, and functions of random vectors. in this paper, we talk about the possibility of using stochastic orders for doing so. we categorize several common stochastic orders and discuss usefulness of this approach for risk comparison.