The one-page case, worked — and the two expense views, side by side

1. One formula — unchanged at v4.0 and v5.0

The formula is the one on the 27 August page. No toolkit arithmetic changed at v4.0. The only symbol added is F, the per-term fixed-expense dollars of the fully-allocated view (Q2); on the default marginal view F = 0 and the formula is exactly the v3.3 one. In plain terms: a customer's value is the sum, year by year, of the margin they earn if they renew, weighted by the chance they are still here, discounted to today. The base variant stops at the bracket; the with-growth variant adds X_i, the expected value of products the customer does not hold yet.

2. Hand-checkable anchor — the flat-retention table from §1.1

Inputs are the Appendix F.1 policyholder's: premium $1,450.00, loss ratio 0.66. The first term carries the 0.40 acquisition expense ratio in place of the 0.20 renewal ratio (paper §3.4), so its margin is −$87.00 ($580.00 of expense against $1,450.00 of premium); the margin in any renewed year is $203.00. Every term, the first included, is discounted at 0.08. Retention is held flat at 90% in one case and 80% in the other — no real book retains at a flat rate, and Section 5 of the paper estimates it properly; the flat rate is what makes every cell checkable with a calculator. (Corrected at v5.1: the v5.0 table charged the acquisition cost in a separate year-0 row and the renewal ratio in year 1 — 0.60 of first-year premium — which contradicted §3.4. Mondello / Robinson, Call #8.)

90% annual retention

80% annual retention

3. Cross-comparison — the two real customers of Figure 1

Same arithmetic, real retention. Two in-force customers from the reference book, valued by the toolkit (B - split 0.40/0.20 expense, residual view, hybrid model). On a one-year view they are the same customer, and B looks marginally better, by $9.28. Over five years A is worth $504.58 more, a ratio of 1.16, and the whole gap is retention.

Figure 1 of paper v5.0 — paper/figures/fig01_two_customers.svg, inlined so this page stays self-contained.

4. How we judge — two expense views, and what each is for

Ron Kozlowski (#112) and AJ Robinson (#111) disagree on fixed expense, and both are right about different questions. The marginal view charges a customer only the cost their presence causes; the fully-allocated view adds each term's share of fixed expense (Economics.fixed_expense_per_term, $75.00 illustrative here). The test we apply: does the view answer the question being asked? For a rating decision the question is how customers differ, and a fixed cost is the same for each of them. For valuing a book the question is what a buyer inherits, and the buyer inherits the overhead.

The Appendix F.1 ten-year renewer under both views

The book under both views — base variant, 8%, five-year horizon

5. The four decisions, each with its actuarial analogue

Q1 — Variant names

The base / with-growth split is the pricing actuary's indicated versus selected: the first is what the customer's own record supports, the second adds a business assumption about future purchases. Single-line describes a product count; the base variant already contains every line the household holds. Ask what the column means for a three-product household and the pair fails.

Q2 — Fixed expense

The same split a rate indication makes between the variable permissible loss ratio and the fixed expense provision. A class relativity is computed without the fixed provision, because it does not vary by class; the overall rate level carries it. Book valuation is the appraisal-value question, and an appraisal includes overhead.

Q3 — Primary use case

One loss-ratio indication serves the rate filing and, summed rather than compared, the planning forecast. The RFP asked for the first; the valuation reading is the same quantity aggregated. Naming both costs one boxed paragraph and one subsection.

Q4 — Basis names

Revenue-neutral is the off-balance step of a class-relativity review: rescale so the book total is unchanged and only the distribution moves. Level-effect is the rate-level change. The old names, filing and planning, named an intended use, so a reader had to remember which use implied which normalisation.

The register ids for the Call #7 asks are R3-1 (the one-page case), R3-2 (two readers), R3-3 (abbreviations and the four-fifths rule), R3-4 (book valuation), R3-5 (no “price optimization”), R3-6 (the §4.4 synthetic-data sentence), R3-7 (ex-ante identifiability, L16), R3-8 (one email, draft plus links) and R3-9 (how the planner is described). Ron's 93 Word comments are RK-2 to RK-91.

6. Glossary

Rendered from scripts/glossary_data.py — the single source of the supplement's Appendix G (the paper's Appendix C carries the 29 core terms) — through scripts/build_glossary.render_html, so this page and the paper cannot define a term two ways. 78 entries, then four specific to this page.

CLV framework

attained tenure

A customer's own tenure at the valuation date, which fixes where on the loss-ratio curve her future years are read from. The tenure multiplier is indexed relative to it, because her observed average loss already embeds the tenure experience she has lived through. Example: A ten-year customer's future multiplier starts from the ten-year point on the curve, so almost none of the remaining descent is credited to her. See also: tenure, loss ratio by tenure.

base variant

The CLV column built from premium, loss and expense only, with no growth assumption; the filing-defensible variant and the one every ratemaking and regulatory exhibit consumes. Toolkit column clv_base; called the unconstrained variant through paper v2.0. Example: A rate-relativity exhibit reads the base variant, so a household's value there does not move if the agency assumes it will later add a second policy. Formerly: unconstrained CLV, clv_unconstrained, filing CLV. See also: with-growth variant, growth value.

book valuation

Summing residual CLV across the in-force book to value the renewal rights as an asset, in the way an annuity portfolio is valued as a reserve. It is a planning figure, not a filing input. Example: An agency principal asking what the renewal book is worth to a buyer is asking for a book valuation. See also: residual CLV, cohort.

cohort

A group of customers reported together, with a mean and an uncertainty band, in place of a per-customer point estimate; the framework reports cohorts by tenure and by rating segment. A segment is a cohort defined by a rating or CLV characteristic rather than by entry year or tenure. Example: Reporting the mean CLV of all households in their fourth to fifth renewal year, with its interquartile band, is reporting a cohort. Formerly: cohort versus segment. See also: behavioral segment, relativity.

cross-sell

The sale of an additional product line to an existing household, treated as a one-time event with an annual chance of happening and credited once, at the modelled time of sale; the value credited is the CLV of the secondary product. Adding it to every renewal term would value one sale as an annuity, which is the defect corrected in paper v3.0. Example: An auto customer who adds a homeowners policy in her third renewal year is a cross-sell, and she cannot add that same second policy again in year four. See also: upsell, growth value.

customer lifetime value (CLV)

The present value of the margin a customer is expected to earn over a stated horizon: in each future year, the expected premium less expected loss and expense, weighted by the probability the customer is still renewing and discounted back to today. It extends the single-term loss projection to the whole relationship. Example: Two households with an identical loss ratio have different CLVs when one is expected to renew for a decade and the other to leave after a single term. See also: present value, survival probability, horizon, base variant.

DERT (discounted expected residual transactions)

The survival-weighted, discounted count of a customer's future renewals: the framework's annuity factor. Differencing it year by year gives the expected number of renewals in each future year, which is what lets a year-varying margin sit inside the CLV sum without any new estimation. Example: A customer with a DERT just under three is expected to produce a little under three renewals' worth of discounted margin over the horizon. See also: survival probability, horizon.

discount rate

The annual rate at which a future year's margin is reduced to its value today, reflecting the cost of waiting for the money. The framework treats it as a sensitivity dimension rather than a fixed truth. Example: At the toolkit's default rate, the tenth renewal term's margin is worth less than half of what an identical margin received this year is worth. See also: present value, horizon.

growth value

The value a household is expected to add through a deliberate business-development action, selling it something it does not hold today; it is the sum of cross-sell and upsell value and is zero in the base variant. It is never premium trend and never the value of existing coverage persisting. Example: The expected value of an auto-only household later buying a homeowners policy is growth value; the auto premium it already pays is not. See also: cross-sell, upsell, with-growth variant.

horizon

The number of future years over which CLV is summed; the toolkit default is five, with a ten-year view available for acquisition decisions. A longer horizon does not rescue a thin margin, because discounting and lapse both shrink the far years. Example: A five-year horizon values only the next five renewals, so a customer expected to stay twenty years is deliberately under-counted. See also: discount rate, DERT (discounted expected residual transactions).

inception CLV

Residual CLV less the acquisition expense: what the customer was worth at the point of sale, and the view an acquisition decision reads. Toolkit column clv_net_of_acquisition; also called new-business CLV. Example: A new customer whose first-year commission exceeds her discounted future margins has a negative inception CLV even though her residual CLV is positive. Formerly: CLV net of acquisition, new-business CLV. See also: residual CLV, expense recovery.

level-effect basis

The tenure curve applied at its own level, so total expected loss falls as the surviving book matures and book CLV rises by exactly the modelled loss saving. For acquisition budgets and retention-spend planning; it must not enter an unfiled indication. Formerly the planning basis through paper v3.2. Example: A retention-spend business case that wants the dollar value of a maturing book reads the level-effect basis. Formerly: planning basis. See also: revenue-neutral basis.

loss ratio by tenure

The measured loss ratio of each attained-tenure cell, smoothed into a curve of multipliers and floored where credibility runs out; the framework applies it relative to each customer's own attained tenure on one of two bases. It is measured on the book, never assumed. Example: The raw yearly ratios are too noisy to price from, so the shipped curve is a premium-weighted fit rather than the observed cell values. See also: revenue-neutral basis, level-effect basis, attained tenure.

off-balance

The correction that rescales a set of relativities so they neither raise nor lower the overall rate level, leaving the aggregate indication to be decided separately. The revenue-neutral basis is an off-balance applied before the relativity is ever reported. Example: Dividing every tenure multiplier by the book's loss-weighted mean is an off-balance. See also: revenue-neutral basis, relativity.

present value

Today's worth of a cash flow that arrives in a future year, obtained by applying the discount rate for each year of delay. CLV is a present value of survival-weighted margins. Example: Margin due in three years is worth less today than the same margin due next year. See also: discount rate.

residual CLV

The value of an in-force customer's remaining renewals, charging renewal expense only, because the acquisition cost has already been spent and cannot be recovered by any decision taken now. It is the view retention decisions read. Example: Deciding how hard to work to keep a renewing customer uses residual CLV, since the commission paid to write her years ago is gone either way. See also: inception CLV, acquisition expense versus renewal expense.

retention allocation

Deciding where to spend retention effort by ranking customers on value at risk rather than on current-term margin. On the reference book a large share of a margin-ranked budget points at the wrong customers. Example: Offering a renewal review to customers in their second and third year, who have paid their acquisition cost but not yet earned it back, is retention allocation. See also: value at risk from churn.

revenue-neutral basis

The tenure curve rescaled so that its loss-weighted mean multiplier is exactly one: a pure relativity that redistributes expected loss across tenure without changing the book total. The toolkit default and the only basis that belongs in a relativity exhibit; formerly the filing basis through paper v3.2. Example: On this basis the book's total CLV cannot move, so a credit to first-year customers is paid for by the longest-tenured cohort. Formerly: filing basis. See also: level-effect basis, off-balance.

tenure

The number of years a household has been continuously insured with the carrier or agency, counted in completed policy terms. Example: A household that first bought a policy six renewals ago has a tenure of six years. See also: attained tenure, tenure seasoning.

tenure seasoning

The improvement in loss experience as a household matures on the book, because it is known, priced with fewer surprises and self-selected to stay. It is a property of the relationship, not of the rate. Example: A household in its eighth renewal runs a lower loss ratio than a first-year risk with the same rating characteristics. See also: loss ratio by tenure, tenure.

upsell

A move to a higher coverage tier or limit within a product the household already holds, treated as a permanent step-up in annual margin from the year of the upgrade onward. A user who projects coverage growth directly into future premium must set the upsell value to zero to avoid counting it twice. Example: A homeowner who raises her dwelling limit and stays at the higher limit every renewal thereafter is an upsell. See also: cross-sell, growth value.

value at risk from churn

The discounted value that leaves if a customer lapses: her CLV multiplied by her probability of not renewing. It is the quantity a retention budget should target, and it differs from current margin. Example: A young customer with a high CLV and a shaky renewal record carries more value at risk than a long-tenured customer who is almost certain to stay. Formerly: value-at-risk, value at risk. See also: retention allocation, churn.

with-growth variant

The CLV column that adds growth value from an explicit cross-sell and upsell program to the base variant; the business-planning view, never a filing input. Toolkit column clv_with_growth; called the constrained variant through paper v2.0, a name actuaries read as regulatorily constrained, which is the opposite of the sense intended. Example: A marketing budget that credits a mono-line household with the chance of adding a homeowners policy reads the with-growth variant. Formerly: constrained CLV, clv_constrained, planning CLV. See also: base variant, growth value, cross-sell, upsell.

Retention and survival models

BG/NBD

Beta-Geometric / Negative Binomial Distribution: a buy-till-you-die model in which each customer renews at her own rate and, after each renewal, has her own chance of leaving for good. It is the probabilistic base of the headline hybrid model. Example: Fitted to the renewal history, BG/NBD gives each household an expected count of future renewals from four parameters shared across the book. See also: Pareto/NBD, BTYD (buy-till-you-die), P(alive).

BTYD (buy-till-you-die)

The family of probabilistic models that counts how many purchases a customer makes before silently ceasing to be a customer; here each renewal is treated as a purchase. BG/NBD and Pareto/NBD are its two members in the toolkit. Example: Treating each annual renewal as one purchase lets a retail purchase-count model value an insurance household. See also: BG/NBD, Pareto/NBD, RFM.

churn

The end of the customer relationship, whether observed as a non-renewal or inferred from a long silence. Insurance churn is observed at each renewal date, which places annual policies on the contractual side of the CLV taxonomy. Example: A household that does not renew at its anniversary has churned. See also: lapse, P(alive).

Cox proportional hazards

A survival model in which each covariate multiplies a shared baseline lapse hazard by a constant factor, leaving the shape of the baseline free. Fitted here on observable covariates only, with no price or rate-change term. Example: Holding more product lines lowers a household's lapse hazard by the same proportion at every tenure in a Cox model. Formerly: Cox proportional-hazards, Cox PH. See also: hazard, Weibull accelerated failure time.

ensemble

A prediction formed by combining several models, here by averaging two gradient boosters. In the toolkit the pure ensemble mode predicts renewals directly, while the hybrid mode uses the same boosters to correct BG/NBD. Example: Averaging the two boosters' renewal predictions gives an ensemble prediction. See also: gradient boosting, hybrid model.

gradient boosting

A machine-learning method that builds many small decision trees in sequence, each correcting the errors of the ones before; a strong predictor on tabular data. The toolkit averages two standard implementations. Example: A boosted model learns that renewal likelihood rises with product count and then refines that rule for large households in particular. Formerly: gradient-boosted. See also: hybrid model, ensemble.

hazard

The rate of lapse at a given tenure among customers still in force at that tenure; the lapse analog of a mortality rate. A falling hazard with tenure is what the survival models measure. Example: If a small share of second-year customers leave at their anniversary, that share is the second-year hazard. See also: survival probability, Cox proportional hazards.

hidden Markov model

A multi-state model whose states are not observed directly but inferred from behavior, so the customer's underlying engagement is a latent variable that the observed renewals reveal. Example: A household that keeps renewing but has stopped adding coverage may be inferred to have moved to a less engaged hidden state. See also: multi-state Markov model, latent variable.

hybrid model

The headline model: BG/NBD supplies each customer's probabilistic per-year renewal expectation and gradient-boosted learners correct only the residual, the part the base model missed. The filing exhibits keep their probabilistic form and the machine learning layer adjusts it. Example: If BG/NBD under-predicts renewals for large households, the residual learner learns that pattern and adds it back. Formerly: residual learner. See also: BG/NBD, gradient boosting, ensemble.

lapse

A policy not renewed at the end of its term; the insurance word for the churn event. In the survival models it is the event whose timing is modelled, and in the Markov model it is the absorbing state. Example: A customer who lets her auto policy expire without replacing it has lapsed. See also: churn, hazard.

multi-state Markov model

A model of year-to-year moves between a small set of customer states, here the number of product lines held plus a lapsed state that cannot be left, summarized in a transition matrix. It captures product-addition dynamics the count models cannot. Example: The chance that a two-product household becomes a one-product household next year is one cell of the transition matrix. Formerly: multi-state model, Markov chain. See also: hidden Markov model, lapse.

P(alive)

A buy-till-you-die model's probability that a customer has not silently left, given her renewal history. A long gap since the last renewal lowers it. Example: A customer who renewed every year until last year has a higher P(alive) than one whose last renewal was three years ago. See also: BG/NBD, churn.

Pareto/NBD

The original buy-till-you-die benchmark: renewals arrive at a customer-specific rate while the customer is active, and the unobserved active lifetime ends at a customer-specific rate. Kept beside BG/NBD so a reader can see whether the ranking depends on the dropout assumption. Example: On the reference book Pareto/NBD and BG/NBD rank customers almost identically even though their dropout mechanics differ. See also: BG/NBD, BTYD (buy-till-you-die).

RFM

Recency, frequency and monetary value: the compact per-customer summary the buy-till-you-die models are fitted on. Frequency is the number of repeat renewals, recency is the timing of the most recent one, and the monetary component here is the customer's average premium and average loss. Example: A household observed for seven years that renewed six times, most recently last year, is one RFM row. See also: BTYD (buy-till-you-die).

Spearman rank correlation

A measure of how closely two rankings agree, ignoring the sizes of the values ranked. The framework uses it to ask whether the six model families order customers the same way, since ranking is what the ratemaking exhibits consume. Example: Two models that put every customer in the same order have a Spearman correlation of one, whatever their dollar values. See also: ensemble, relativity.

survival probability

The probability that a customer is still renewing at a given future term; the retention analog of survival in a life table. It is the weight on each future year's margin in the CLV sum. Example: A customer who renews nine years in ten has a survival probability to the second future term of a little over four in five. See also: hazard, DERT (discounted expected residual transactions).

Weibull accelerated failure time

A parametric survival model in which covariates stretch or compress the time to lapse, with the lifetime following a Weibull distribution. It is the toolkit's second survival specification. Example: In a Weibull model a larger household is expected to stay a fixed multiple longer than a smaller one, all else equal. Formerly: Weibull accelerated-failure-time, Weibull AFT. See also: Cox proportional hazards, hazard.

Data and calibration

behavioral segment

A descriptive label the generator draws for each household, such as price-sensitive, loyal multi-product or growing business. In the reference book the outcomes are driven by the three latent fields, not by the label, and it is never a rating variable. Example: A household drawn from the loyal multi-product segment renews more reliably and adds products more often than one from the price-sensitive segment. See also: latent variable, cohort.

calibration band

A permitted range for a generated statistic, anchored to a loaded public benchmark, such as average premium, claim frequency or loss ratio by product line. The bands are data in the toolkit, not prose in the paper. Example: Homeowners claim frequency on the generated book must fall inside the band anchored to the published share of insured homes that claim each year. See also: realism check, reference book.

latent variable

A quantity that drives the data but is not observed in it, such as a household's true retention propensity or risk level. The generator knows its latent variables, which is what makes parameter recovery possible. Example: A household's underlying risk factor sets its claim frequency, but only the claims are visible to the models. Formerly: latent. See also: parameter recovery, behavioral segment.

loss development factor (LDF)

The multiplier that carries a reported loss to its expected ultimate value, by claim maturity. The generator's reported losses are its ultimate losses divided by a cumulative development factor drawn from stylized public patterns. Example: A one-year-old homeowners claim needs a smaller development factor than a one-year-old liability claim. See also: ultimate loss, Schedule P.

parameter recovery

Fitting a model to synthetic data and checking that it recovers the retention the data was generated with; a validation real data cannot offer because the truth is known. The gate compares each family's one-year in-force renewal rate to the book's empirical rate within a stated tolerance. Example: A survival model that predicts nearly the same in-force renewal rate the generator used has recovered the parameter. See also: latent variable, realism check.

realism check

The automated test that fails the build if any generated statistic leaves its calibration band or if a structural property of the book, such as tenure seasoning, is absent. Realism is asserted by a test, not claimed in documentation. Example: A change to the generator that pushed commercial premium above its band would fail continuous integration before it reached the paper. See also: calibration band, drift gate.

reference book

The seeded synthetic book on which every figure in the paper is produced: five thousand households over eleven policy years, generated with the toolkit's default configuration. No proprietary data enters the repository, so the reference book is also the only book a reader needs to reproduce the paper. Example: Re-running the generator with the default configuration produces the reference book byte for byte. Formerly: synthetic book. See also: seed, calibration band.

Schedule P

The loss-reserving exhibit of the NAIC annual statement, organised by accident year; the CAS Loss Reserving Database is derived from it. It is the source of the stylized development patterns and shows why tenure cannot be studied on public data: it carries no policyholder tenure. Example: A carrier's private-passenger-auto triangle of paid and incurred loss by accident year is a Schedule P exhibit. See also: loss development factor (LDF), ultimate loss.

ultimate loss

The fully developed cost of a claim once all payments are known, as opposed to the reported amount, which is the case-reported figure at the observation date. The toolkit carries both and defaults to ultimate. Example: A liability claim reported at a modest case reserve may develop to a much larger ultimate loss over several years. Formerly: reported loss, ultimate versus reported loss. See also: loss development factor (LDF), Schedule P.

Ratemaking

classical credibility

The weight given to a segment's own experience against the book, rising with the segment's claim count until the full-credibility standard is reached and capped at one. The complement of the weight is applied to the book relativity of one. Example: A segment with few claims keeps most of the book's relativity; a segment with many claims is trusted on its own. See also: full-credibility standard, square-root rule, exposure base.

expected lifetime

The expected number of future policy years a segment's customers will remain, obtained by summing the segment's survival probabilities over the horizon; the denominator behind the retention-adjusted loss ratio. Example: A multi-line segment expected to stay almost eight years against under three for mono-line has the longer expected lifetime. See also: retention-adjusted loss ratio, survival probability.

expense recovery

The schedule showing how a new customer's acquisition expense, charged in the first year, is recovered from survival-weighted, discounted renewal margins, and the breakeven year in which cumulative margin first turns positive. The breakeven year moves with the acquisition load. Example: A customer who lapses after two terms never reaches the year in which her first-year commission would have been recovered. Formerly: payback. See also: inception CLV, acquisition expense versus renewal expense.

exposure base

The unit counted when measuring a segment's credibility: claim counts in the toolkit, against the claim-count standard. A customer-count base is retained only to reproduce earlier figures, because on equal-size quantiles it yields the same credibility in every row and carries no information. Example: Five equal-size CLV quintiles differ in credibility on a claims base and are identical on a customer base. Formerly: claims versus customers exposure base. See also: classical credibility.

full-credibility standard

The number of claims at which a segment's observed frequency is judged reliable enough to stand alone: the classical standard used here is the count for which observed frequency sits within a small band of expectation with high probability. It is a claim-count standard and has no interpretation as a number of customers. Example: A segment whose claim count reaches the standard receives a credibility of one. See also: classical credibility, square-root rule.

loss ratio

Incurred loss divided by earned premium over the same period. In this paper it includes allocated loss adjustment expense unless stated otherwise. Example: A segment that pays out a little over half of the premium it collects in claims has a loss ratio a little over one half. See also: loss-ratio basis, ALAE.

loss-ratio basis

Computing a segment's indicated relativity as its loss ratio divided by the book loss ratio, so the factor correlates with expected loss rather than with profitability or willingness to pay. This is what makes a CLV-segment relativity filing-defensible. Example: A high-CLV segment earns a credit only because its loss ratio is lower, not because its customers are valuable. See also: relativity, base variant.

relativity

The factor by which a rating cell's rate differs from the base, deciding how a given amount of expected loss is allocated across cells; it cannot by itself decide how much expected loss there is. The toolkit's relativities are on a loss-ratio basis and credibility-weighted. Example: A relativity below one for a segment means that segment is charged less than the book average for the same exposure. See also: loss-ratio basis, classical credibility, off-balance.

retention-adjusted loss ratio

The lifetime loss ratio of a segment: loss by tenure year weighted by the segment's own expected survival to that year, summed, divided by premium weighted the same way. It is a ratio of weighted totals, not a weighted mean of ratios, and its book row depends on the segmentation because each segment is carried on its own survival curve. Example: A segment with the worst first-term loss ratio of three can still indicate a credit once its longer expected life is weighted in. See also: expected lifetime, survival probability, relativity.

square-root rule

Partial credibility equal to the square root of the segment's claim count divided by the full-credibility standard, capped at one. Example: A segment with one quarter of the standard's claims receives one half credibility. Formerly: square-root credibility. See also: classical credibility, full-credibility standard.

Regulatory

adverse-impact ratio

A group's favorable-outcome rate divided by the reference group's, where favorable means a CLV above the book median. The screen flags any ratio below the four-fifths threshold. Example: A group with the same favorable rate as the reference group has an adverse-impact ratio of one. See also: four-fifths rule, reference group.

disparate impact

An outcome that falls unevenly across groups defined by a protected characteristic or its proxy, regardless of intent. The toolkit screens for it; a flagged factor needs an expected-loss rationale to survive, and the screen is not a causal test. Example: If one region's households are markedly less likely to receive a favorable CLV than the largest region's, the screen reports a disparate impact. See also: four-fifths rule, adverse-impact ratio, proxy.

four-fifths rule

The convention, borrowed from employment law and echoed in insurance guidance, that a group's rate of favorable outcomes should be at least four fifths of the reference group's. Below that line the factor is flagged for review. Example: A group whose favorable rate is three quarters of the reference group's fails the four-fifths rule. See also: adverse-impact ratio, reference group.

prior approval

A filing regime in which rates must be approved by the regulator before use, as in California; contrasted with file-and-use, in which rates take effect on filing with actuarial support kept on file, as in Texas. Both require a cost-based justification for any relativity the toolkit produces. Example: A carrier in a prior-approval state waits for the regulator's decision before charging a new tenure relativity. Formerly: file-and-use. See also: relativity, loss-ratio basis.

proxy

An observable variable that stands in for a protected characteristic the data does not carry, such as region or age band. The screen is run across proxies because tenure correlates with age, so any move toward a tenure relativity needs the age-band screen. Example: Age band is used as a proxy because the data records age but not any protected class directly. See also: disparate impact, reference group.

rate adequacy

Whether charged premium covers expected loss plus expense and a profit provision; the toolkit compares charged premium to the indicated premium and labels the ratio inadequate, adequate or potentially excessive using exhibit conventions, not statutes. The revenue-neutral basis leaves the verdict unchanged by construction. Example: A segment whose premium falls well short of its indicated premium is labeled inadequate. See also: revenue-neutral basis, relativity.

reference group

The group against which every other group's favorable rate is compared in the disparate-impact screen; the largest group by default, and always stated on the exhibit. Example: When the Southeast holds the most households, the Southeast is the reference group for the region screen. See also: adverse-impact ratio, proxy.

Economics and expenses

acquisition expense versus renewal expense

New business carries acquisition expense (first-year commission, underwriting, inspection, marketing) that renewals do not, so the expense ratio is higher in the first term than thereafter. Residual CLV charges renewal expense only; inception CLV charges both. Example: An agency pays a higher commission on a policy it writes than on one it renews. Formerly: acquisition expense, renewal expense. See also: residual CLV, inception CLV, expense recovery.

ALAE

Allocated loss adjustment expense: the cost of handling a specific claim, such as defense counsel or an adjuster's fee. It attaches to claims and belongs in the loss projection, which is where the toolkit's generator already carries it. Example: The legal fees on a single liability claim are ALAE. See also: ULAE, loss ratio.

fixed versus variable expense

Variable expense scales with premium (commission, premium tax, premium-proportional servicing) and is what the toolkit's expense ratios represent; fixed expense is incurred regardless of any one customer. Only genuinely avoidable per-policy dollars may be entered as fixed amounts in the toolkit. Example: Commission is variable; the systems budget is fixed; a per-policy inspection fee that is not paid on a declined risk is avoidable and may be charged. See also: marginal expense view, acquisition expense versus renewal expense.

fully-allocated expense view

The alternative reported view in which each policy-term also carries a share of fixed overhead, through the toolkit's fixed-expense-per-term setting. It is the lens for valuing a whole book, because a buyer inherits the overhead; it ranks customers as the marginal view does and differs from it in level. The choice of default view was put to the Project Oversight Group in September 2026. Example: Loading each policy-term with a share of the home-office lease before computing the customer's value is the fully-allocated view. Formerly: fully-allocated view. See also: marginal expense view, fixed versus variable expense, book valuation.

marginal expense view

Charging a customer only the expense that would not be incurred if she were not written. A CLV is a marginal calculation by design, so fixed overhead stays out of it and belongs in the overall rate level instead. Example: The underwriting time spent on one application is marginal; the cost of the actuarial department is not. Formerly: marginal view. See also: fully-allocated expense view, fixed versus variable expense.

ULAE

Unallocated loss adjustment expense: the cost of running the claims operation that cannot be tied to one claim. It is a servicing cost and belongs in the expense ratio, not in the loss projection. Example: The salaries of the claims department are ULAE. See also: ALAE, fixed versus variable expense.

Reproducibility and software

drift gate

The check that every number printed in the paper was produced by the toolkit: it extracts each numeric literal from the manuscript, prose and table cells alike, and matches it against the seeded payload or a register of cited external figures. An unmatched number fails the build. Example: A table hand-copied from an older run fails the gate, because its cells no longer match the payload. See also: seed, realism check.

MPL 2.0

The Mozilla Public License, version two: the open-source license the toolkit is released under, which permits commercial use and requires that changes to the licensed files themselves be shared. Example: A carrier may embed the toolkit in a proprietary pricing system and must publish only its modifications to the toolkit's own files. See also: notebook.

named scenario

A labeled bundle of assumption changes run on the headline model, such as a soft market, a hard market, adverse retention, a recession or a long horizon, so that a reader can see the book's value under a story rather than under one parameter at a time. Example: The adverse-retention scenario lowers every customer's renewal probability by the same proportion and reports the resulting book CLV. See also: sensitivity grid.

notebook

One of the six companion Jupyter notebooks that walk through the toolkit on the reference book, from data exploration to a full worked example. Each is pinned to the paper's book so a reader reproducing a figure from a notebook gets the paper's number. Example: The full-worked-example notebook fits all six families and builds a filing exhibit package for two states. See also: reference book, seed.

seed

The fixed starting value given to every random number generator so that the synthetic book, every fit and every figure re-run identically. Every modelling script in the toolkit sets the same seed first. Example: Two readers on two machines who run the generator with the shipped seed obtain the same five thousand households. Formerly: deterministic reproduction. See also: reference book, drift gate.

sensitivity grid

A sweep of one or more assumptions across a bounded set of values, reported as the change in book CLV; the one-way version is drawn as a tornado chart, widest bar at the top. Conclusions are meant to survive the grid, not to hinge on the point estimates. Example: Sweeping the discount rate and the renewal expense ratio together and tabulating the book total for each pair is a sensitivity grid. Formerly: tornado. See also: named scenario, discount rate.

Terms specific to this page

Ex-ante identifiability (L16)

Whether a high-value customer can be recognised at inception from covariates and history, rather than in hindsight. Kozlowski, Call #7: “Ron Kozlowski was a great risk … but do we know that ahead of time?” Recorded as limitation L16 in v4.0; not tested here.

Marginal vs fully-allocated view

Two expense views of the same CLV. Marginal charges variable expense only (the default; for rating decisions). Fully-allocated adds a fixed dollar amount per policy term through Economics.fixed_expense_per_term (for valuing a book). They differ by that amount × DERT.

Paper and Technical Supplement

From v5.0 the two readers are served by two documents rather than two reading paths: the paper (59 pp) carries the argument and the exhibits in plain language, and the Technical Supplement (51 pp), numbered section for section, carries the formulas, the data dictionary and every exhibit worked by hand. Section 1.5 of the paper, Where the detail lives, explains the split.

RK-n / R3-n / Word #n

Register ids. RK-n is one of Kozlowski's written comments (RK-2 to RK-91), each mapped to its Word comment number (#12 to #184); R3-n is a verbal ask from Call #7. All live in review_responses.html.