Ratemaking

Loss and premium experience is given along with a target loss ratio and an indication is needed.

Loss ratio method: indicated rate change = (experience loss ratio at present rates × trend / target loss ratio) - 1. Pure premium method: indicated rate = (trended losses per exposure + fixed expense per exposure) / (1 - variable expense ratio - profit). Use the same trend assumptions in both methods. Pure premium method requires accurate exposure data; loss ratio method does not.

LR method: rate change = (LR_present_rates / target_LR) - 1. PP method: rate = (PP + F) / (1 - V - Q).

Historical losses and premiums are given for several accident years and you must trend each to the future policy period.

Compute annual trend rates from data (or use a specified trend). Apply trend exponentially from the historical mid-period to the future mid-period. Premium trend captures changes in exposure mix (e.g., rising auto values); on-leveling adjusts past premiums to current rates. Adjust losses for benefit changes (e.g., medical inflation, deductible changes) before applying trend.

Trend factor = (1 + trend)^{years from historical to future mid-period}.

A multi-coverage product has fixed and variable expenses, and you must compute the rate for each coverage.

Identify fixed expenses (allocated by exposure or coverage) and variable expenses (allocated by premium). Allocate fixed expenses to each coverage based on policy counts or exposure. Use variable expense ratios on a per-coverage basis. Add a profit provision Q (target underwriting return on premium); plug into the pure premium formula.

Variable expense allocation = ratio × premium; fixed expense allocation by exposure.