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This guide takes three accident years of synthetic collision experience to an indicated overall rate change. Every amount stays an exact Decimal from the paid losses to the indication.

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Develop losses to ultimate

Build a triangle from one row per accident year and age. Ages are months of development, and values are cumulative paid losses and loss adjustment expenses (LAE):
factors averages each column of link ratios. volume divides the sum of later values by the sum of earlier values; simple averages the ratios. periods=3 keeps the latest three origins for each pair of ages. The last row is the tail factor from 36 months to ultimate. The factors table is your selection. To select a factor yourself, edit its factor cell in pandas. develop reads age and factor, and recalculates each cumulative factor:
unreported holds ultimate less latest: unpaid losses for a paid triangle, IBNR for a reported one.

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Bring premium to current rates

Record each overall rate change by its effective date. on_level gives the parallelogram factor for each calendar year of earned premium, for annual policies written evenly through the year:
A date counts the days elapsed in its year, so 1 July 2021 is 181/365 of the way through 2021. For the textbook’s mid-year, write D("2021.5") as the effective point. basis="written" gives factors for written premium, and term_months sets another policy term. To rate each historical policy again at current rates, use Program.rate with the current program; that gives exact on-level premium policy by policy.

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Fit a trend

Fit an annual exponential trend to quarterly average severity. Each period is a number of years, or a date:
trend.observations holds each quarter with its fitted value. For a selected trend, write Trend(D("0.04")). trend.factor(start, end) projects from one point in time to another.

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Calculate the indication

Trend each year’s ultimate losses from its average accident date to the average accident date of the future policy period. Divide by on-level earned premium:
Give the expense and profit provisions as shares of premium:
The experience indicates a 3.36% increase: (loss_ratio + fixed_expense) / (1 - variable_expense - profit) - 1.

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Weight the indication by credibility

Blend the indication with a complement, such as the trended change since the last review. credibility gives limited fluctuation credibility from a claim count, with 1,082 claims for full credibility:
860 claims give 89% credibility, and the credibility-weighted change is 3.32%. full_credibility(probability=..., tolerance=...) gives the standard for other choices. To spread the change across rating factors, fit relativities from experience.