Customer Lifetime Value is the expected present value of a P&C customer's future underwriting cash flows — premium net of losses and expenses — across the multi-year renewal relationship, weighted at each renewal by the probability the customer is still with us.
Three commitments this definition bakes in — i.e. how the work is framed:
X term) is business-optimization, carved out of rate indications in strict jurisdictions
(NY §2304). Regulatory defensibility is a design constraint from day one.predict_clv() contract — the
probabilistic form drives the filing exhibits.Asking POG to confirm three conventions that change the exhibits: (a) residual vs total CLV horizon · (b) discount-rate basis (prescribed / risk-free + margin / sensitivity-only) · (c) cross-sell excluded from rate indications across all target states or only the strict ones.
CLV supplements single-term loss projection with a multi-horizon view of the customer relationship. For customer i over horizon T years, discounted at rate d:
| Term | Meaning | Where it comes from |
|---|---|---|
| S(t) | Survival / retention probability to term t — the renewal analog of survival in life | Brockett 2008 · Dong–Frees 2022 |
| P(t) | Expected premium (grows with tenure / coverage) | Gupta 2004 (margin core) |
| L(t) | Expected losses in term t | actuarial loss linkage |
| E(t) | Expenses (acquisition, servicing) | Gupta 2004 |
| X(t) | Cross-sell / referral value business-optimization only | Verhoef–Donkers 2001 |
| Cohort, not point estimate | CLV is structurally an actuarial annuity with retention as survival — so we report segment/cohort CLV with uncertainty bands, not false-precision per-customer dollars. (Orliński 2026 annuity analog.) |
| Actuarial vs business-optimization split | Filing-eligible: retention-adjusted loss ratios, tenure-correlated loss differences
(must correlate with expected loss). Operational only: cross-sell / referral value (the
X term) — excluded from rate indications in strict jurisdictions (NY §2304). |
The single CLV equation is reported as two side-by-side columns: an base variant valuing the renewal book as-is (P − L − E, with X = 0), and a with-growth variant that additionally counts explicit cross-sell + upsell value (the X term made concrete).
clv_base — the filing-defensible base; coincides
with the "actuarially justified" side of the bright line; the rate-side number in strict
jurisdictions (NY §2304).clv_with_growth — the business-planning view under explicit
cross-sell (products added to the household — Verhoef–Donkers 2001 potential value) and
upsell (coverage-tier / limit upgrades — the Markov transition dynamics) assumptions; for
marketing, distribution and agency management.predict_clv() returns both columns;
sensitivity_analysis() sweeps cross-sell and upsell as explicit grid dimensions.Labels settled on POG review, 16 Aug 2026. These columns were
clv_unconstrained / clv_constrained through paper v2.0. AJ Robinson's
review established that actuaries read "constrained" as regulatorily constrained — the
filing-safe variant — which is the opposite of the sense intended. Since the word is ambiguous
in the direction it points, flipping it would have preserved the ambiguity; the pair was renamed
to the neutral base / with growth. The old column names remain as deprecated aliases for
one release, so nothing that already runs breaks. The decomposition itself is unchanged.
predict_clv() contract across families| Family | Captures | Toolkit class | Status |
|---|---|---|---|
| Contractual probabilistic | Renewal-cycle retention (each renewal = purchase occasion) | BGNBD_CLV, ParetoNBD_CLV | BG/NBD ✓ |
| Survival | Time-to-lapse hazard | Cox PH / AFT | next |
| Multi-product transition | Coverage-tier / product-addition dynamics | MarkovCLV, HMM | Phase 3 |
| Predictive ML | 3yr/5yr value from rich features | EnsembleCLV (XGBoost/LightGBM) | Phase 3 |
| Hybrid (headline) | BG/NBD base + ML residual correction; probabilistic form for filings | EnsembleCLV (hybrid mode) | POG-selected |
16-paper corpus organized into four research streams. For each reference: what we took into the framework — not just that it was read.
| Reference | What we took into the framework | Feeds |
|---|---|---|
| Gupta, Lehmann & Stuart (2004) valuation |
The discounted retention–margin core of CLVi (we generalize their
scalar margin to time-varying P−L−E+X); cohort-reporting discipline; retention as the
dominant value lever → why we run retention sensitivities first. |
CLV_i skeleton |
| Verhoef & Donkers (2001) valuation |
Current-vs-potential value framing for segmentation; justification for the
X (cross-sell) term as forecastable. Caveat carried forward: business-optimization,
stays out of strict-state rate indications. |
cross_sell_adjusted_premium() |
| Brockett et al. (2008) survival |
Household/portfolio grain for retention (not policy-level); the logistic + survival (hazard)
specification for the S(t) term; "first-cancellation → total-defection window" → treat
partial lapse as an early-warning state. |
Cox PH / AFT survival |
| Guillén, Pérez-Marín & Guelman (2013) survival |
The explicit retention ↔ price-elasticity ↔ profit linkage; heterogeneous-treatment framing for the proposal's "retention credit". Caveat: grey-lit presentation — cite peer-reviewed companions. | clv_rate_relativities(),retention_adjusted_loss_ratio() |
| Dong, Frees, Huang & Hui (2022) multi-state |
Direct template for MarkovCLV (coverage-tier transitions) + HMM latent-state extension;
2nd-order-Markov MLR as a benchmark row. The paper's own claim — multi-state retention yields
more accurate CLV. Closest actuarial anchor. |
MarkovCLV, HMM |
| Schmittlein, Morrison & Colombo (1987) BTYD |
Foundational "buy-till-you-die" precedent for ParetoNBD_CLV (native hyp2f1,
next in queue) and conceptual parent of the BG/NBD base. |
ParetoNBD_CLV |
| Fader, Hardie & Lee (2005) BTYD |
Direct basis for BGNBD_CLV — built & tested. Closed-form log-likelihood +
eq.10 expectation via hyp2f1 + discounted DERT; each renewal = a purchase occasion.
The probabilistic base of the hybrid headline model. |
BGNBD_CLV ✓ |
| Haddadi & Hamidi (2025) ML |
Closest published template for the headline architecture — named support for
EnsembleCLV and the hybrid (BG/NBD base + ML residual). Our answer to "is the hybrid
grounded in the literature?" |
EnsembleCLV (hybrid) |
| Wong, Viloria Garcia & Lim (2025) ML |
Empirical precedent for probability + ML in a non-contractual setting; supports framing insurance renewals as purchase occasions. | hybrid validation |
| Mahdiyasa, Pasaribu & Sari (2025) multi-state |
Validated insurance precedent for MarkovCLV (active/upgraded/lapsed + survival).
(= the proposal's mis-cited "Widyawan et al. 2025".) |
MarkovCLV |
| Jena et al. ML |
A plain-regression CLV baseline for the model-comparison table — the contrast that shows what a deployable regressor gives up vs. probabilistic + hybrid models. | comparison baseline |
| Orliński (2026) practitioner |
The annuity analog and skeptical discipline — CLV as a relative signal, reported at cohort grain with uncertainty bands, not false-precision dollars. | cohort-reporting design |
| CAS (2004 & 2014) CAS precedent |
CAS's own precedent that CLV belongs in P&C pricing over a multi-renewal horizon under regulatory constraint — establishing that the gap we fill is an implementation-ready, reproducible toolkit, not the concept. (Exact works to confirm with POG.) | positioning / gap |
| Parr Rud (2001) practitioner |
Practitioner LTV-scoring lineage (SUGI/SAS) — a "before" contrast point showing how far the field predates a regulator-ready, reproducible framework. | related work / contrast |
| Balona (2025) governance |
Grounds the AI-usage disclosure discipline (docs/ai_usage_log.md, a contract
requirement) and responsible-AI framing in the methodology section. |
AI disclosure / methods |
The synthesis: marketing CLV gives the valuation skeleton; insurance survival/multi-state gives insurance-grade retention dynamics; BTYD gives the probabilistic engine; the 2025 hybrid papers give the named template. None ships a regulator-ready, reproducible ratemaking toolkit — that is our contribution.
VALIDATE assumptions baked into the framework that we'd like POG to confirm · DECIDE genuine design choices where POG steer now saves rework before Phase 3/4 deepen.
X term is business-optimization only. Confirm exclusion from rate
indications across all target states (CA/TX/NY/CO), or only strict NY with others allowed?| Dropped reference | Proposal ref "Bolaños/Guillén/Nielsen 2012 (JRI)" couldn't be located/confirmed; substitute scan was image-only. Dropped — Guillén et al. (2013) covers the same Barcelona-group ground. |
| Citation corrections | "Widyawan et al. (2025)" = Mahdiyasa et al. (2025); "Wardani et al. (2015)" = the ITB-Bandung 2015 AIP paper, superseded by Mahdiyasa 2025. Ask POG to confirm the exact CAS 2004/2014 works. |