The whole paper in six case studies

CAS CLV Pricing · a simplified, visual walkthrough · every figure reproducible (set_seed(42)) and publicly anchored

How the six stories tile the paper

One individual customer, then seven cohort views (the annuity-analog discipline says quote the cohort, not the point). Cases 5–8 give the four customer-cohort lenses a reviewer can slice the book by — tenure, multi-product, producer book, and geography. Each case answers one question in plain language and covers one part of the paper.

#	Case study	Grain	The one-line takeaway	Paper
1	Maria Chen — one customer, six models	individual	Six unrelated models value the same customer within ±9%.	§4, §6
2	CLV segments → loss-ratio gradient	cohort	CLV rank tracks loss cost (1.73 → 0.17) — so it's filing-relevant.	§7.1
3	Cross-sell — filing vs planning	cohort	Growth value is a separate, auditable $693/customer — never in a rate.	§2.1, §8
4	New business is written at a loss	cohort	Year-1 margin is a fraction of year-2; acquisition is recouped over renewals.	§4.3, §7.4
5	Seasoning — loss ratio by tenure	cohort	Early years run worse; the lifetime view weights them by certainty.	§7.2
6	Multi-product cohorts	cohort	Each added product cuts the lapse hazard — cross-sell buys persistence.	§6, retention
7	Producer-book cohorts	cohort	Books vary ~2× in value; 20% of it sits with lapse-adjacent customers.	§7 agency mgmt
8	Geography cohorts	cohort	Regional CLV tracks loss ratio — and passes the four-fifths fairness screen.	§8 regulatory

1Maria Chen — one customer, six modelsINDIVIDUAL covers §4 framework · §6 models

If six different models disagree, why trust any of them?

Maria is the proposal's illustrative customer, cast into the book: a 2-product household (auto + home), tenure 5, coverage tier 2, a clean low-risk file (claims ≈ $0), combined premium ≈ $3,428. Her 5-year filing CLV under all six families:

Filing (unconstrained) CLV, 5-yr horizon, 8% discount. Spread $8,632–$10,343 — ±9% of the mean.

The discipline in one number: the models agree, but a single customer is still a point estimate on an unvalidated churn table. So we quote the cohort: Maria's cohort (auto+home, tenure 4–5, tier ≥2; n=55) has a mean planning CLV of $3,054 with a wide P25–P75 of −$801 to $7,018. That range — not Maria's $9.5k point — is the honest exhibit. Cases 2–6 are all cohort views for exactly this reason.

Reproduce: python docs/calls/case_studies_data.py (Case 1).

2CLV segments → the loss-ratio gradientCOHORT · 5 quintiles covers §7.1 ratemaking

Is a CLV segmentation actually about loss cost — or just willingness to pay?

Rank the book into five equal segments by filing CLV and read each segment's loss ratio. The gradient is monotone at the extremes — the bottom quintile destroys value at a 1.73 loss ratio (mean CLV −$10,496), the top runs at 0.17 (mean CLV +$14,850):

■ Q1 loss ratio > 1.0 destroys value. The 10-to-1 gradient is the point: CLV segments are loss-informative, which is what makes them legitimate organized cost experience.

The credibility-weighted relativity runs 3.01 (Q1) down to 0.34 (Q5) — and it is indicated by the loss-ratio column alone, so it would hold under any labeling. That is the filing-defensible use of CLV.

Reproduce: case_studies_data.py (Case 2) → clv_rate_relativities; paper §7.1.

3Cross-sell — filing vs planningCOHORT · whole book covers §2.1 two-variant · §8 regulatory

Where does the value of a cross-sell program go — and does it touch a rate?

Every CLV comes in two versions from the identical calculation. The filing variant is the renewal book as it stands (P − L − E). The planning variant adds the value of growth you hope for (cross-sell + upsell). The gap between them is an exact, auditable dollar figure:

Filing base (P − L − E) — filing-defensibleGrowth value (cross-sell + upsell) — planning only

Book mean per customer: filing $2,805, planning $3,499, gap $693. Because both come from the same calculation, a regulator can verify to the dollar that none of the green is in the filing (NY §2304 / CA Prop 103).

Reproduce: case_studies_data.py (Case 3); paper §2.1, §8.

4New business is written at a lossCOHORT · new-customer avg covers §4.3 · §7.4 expense timing

Why does splitting acquisition vs renewal expense change the story?

Acquiring a customer costs far more than renewing one (40% of first-year premium vs 20% after). For one new customer (avg premium $4,013, loss $2,249, retention 0.934), the cumulative discounted margin climbs over the relationship:

Cumulative discounted margin, one new customer. Year-1 margin is only $159 vs $898 in year 2 — acquisition consumes most of the first year's contribution; it is recouped over renewals to $4,641 by year 10.

On this book, at the default 0.40 acquisition ratio the customer breaks even within year 1; the classic "written at a loss" pattern deepens as acquisition cost rises (breakeven moves to year 2 near 0.55). Charging a renewal the sunk acquisition cost would understate the in-force book by ~$573/customer (§4.3).

Reproduce: case_studies_data.py (Case 4) → expense_recovery_exhibit.

5Seasoning — loss ratio by tenureCOHORT · tenure bands covers §7.2 retention-adjusted LR

Does a customer's loss experience change as the relationship ages?

Loss ratio by tenure year shows clear seasoning: new business runs hot (0.63 at tenure 0), settling into the low 0.40s by tenure 8+. Weighting each year's loss ratio by the certainty of reaching it gives the survival-weighted lifetime loss ratio of 0.536, above the pooled 0.525 — because the early, worse years are the ones you are sure to experience:

Loss ratio by tenure year (x-axis = years since inception). The lifetime view is the correction a single-term analysis misses.

Reproduce: case_studies_data.py (Case 5) → retention_adjusted_loss_ratio.

6Multi-product cohortsCOHORT · # products held covers §6 multi-state · retention linkage

Does cross-selling actually make customers stay — or just add premium?

The fitted product-state Markov model gives the annual lapse hazard for each product-count state directly. It falls sharply as the household holds more products:

Annual probability of lapse by number of products held. Each added product roughly halves the churn hazard — so a cross-sell dollar buys persistence, not just premium. This is the retention linkage the multi-state and hybrid models exploit.

Reproduce: case_studies_data.py (Case 6) → MarkovCLV.transition_.

7Producer-book cohortsCOHORT · by producer covers §7 agency management

Which producer's book is worth the most — and how much of it is about to walk?

Group every customer under their producer (12 books here). Each book's value is the sum of its customers' CLV; the at-risk slice is the value tied up in in-force customers whose renewal outlook is in the bottom quartile — the ones a retention call should reach first.

Book CLV (5-yr, planning) At-risk slice (lapse-adjacent customers)

12 producer books range $967K–$1,799K (≈2×). About 20% of total book value sits with lapse-adjacent customers — a ranked, dollar-weighted retention worklist per producer.

Reproduce: case_studies_data.py (Case 7). Producer assignment is a deterministic synthetic split (customer_id % 12); paper §7 / notebook 05.

8Geography cohortsCOHORT · by region covers §8 regulatory (fairness screen)

Does CLV differ by region — and is that difference fair?

Mean CLV by region tracks the region's loss experience: FL and CA (loss ratios ~0.51–0.53) sit highest, NY and GA (~0.60) lowest. So the CLV difference is a loss-cost difference, not a geographic preference:

Mean 5-yr CLV by region, with each region's loss ratio. Higher loss ratio → lower CLV, exactly as it should.

And is it fair? The built-in adverse-impact screen (a customer is a "favorable outcome" if their CLV is above the book median) compares each region's favorable rate to the largest region's. Every region lands between 0.98 and 1.03 — the lowest is 0.98, well above the four-fifths (0.80) bar — so no region is flagged. The regional CLV spread is loss-driven, not an adverse-impact problem.

Reproduce: case_studies_data.py (Case 8) → disparate_impact_test; paper §8.

Reproducibility & provenance

Every toolkit figure on this page is printed by python docs/calls/case_studies_data.py on the seeded synthetic book (set_seed(42), 5,000 households, 2015–2025). Public anchors (premiums, loss ratios, expense, retention, discount) are each cited to a loaded primary source in research/data/calibration_benchmarks.md. Synthetic data only — no proprietary data. Full detail: worked examples · the paper (§4–§8).