Generalized Earned Premium Rate Adjustment Factors

The loss ratio method of ratemaking requires the Actuary to adjust earned premiums to reflect all rate changes that have been implemented. Many Actuaries use the parallelogram method of finding the portion of the exposures earned from a given rate change. The assumption is made that exposures ace being written at is constant level. Computers are becoming an indispensable tool for the Actuary and the parallelogram method is cumbersome for computer applications. The purpose of this paper is to derive a simple general formula for finding the earned portion of a rate increase for any given policy term, rate Effective date, and evaluation period (period during which the premiums are earned). In the latter portion of the paper a formula is given based on the assumption that exposures are increasing at a given growth rate. Finally, a comparison is made of results produced by the constant exposure model versus the constant growth rate model.