What does identically distributed mean in an insurance context?

In the context of insurance, "identically distributed" refers to a situation where each exposure faces the same probabilities of loss. This terminology is rooted in the statistical principle that when exposures are identically distributed, they share the same distribution characteristics, meaning that the likelihood of experiencing a loss, as well as the nature and severity of those losses, are the same across all exposures.

This concept is critical in actuarial science and risk management because it allows insurers to apply general statistical models to predict loss outcomes. When exposures are assumed to be identically distributed, it enables the insurer to utilize aggregate data to create more accurate pricing models and establish reserves since they can rely on the consistency of risk among the collected data.

In essence, this uniformity simplifies the calculations involved in underwriting and helps in developing an equitable approach to premium setting, reflecting the same risk level across the board for similar exposures. This foundation leads to a more streamlined process in risk assessment and management within the insurance industry.