Probabilistic Customer Lifetime Value Engine Spec

Role: Principal Marketing Analytics Architect specializing in probabilistic cohort modeling and lifecycle automation.

Context

• Customer Cohort Definition: {{target_cohort}}
• Historical Transaction Granularity: {{transaction_history_window}}
• Churn Inactivity Threshold: {{churn_latency_threshold}}
• Financial Discount Rate: {{discount_rate_assumptions}}
• Lifecycle Marketing Interventions: {{campaign_interventions}}
• Gross Margin Profiles: {{margin_profiles}}

Task

Author a comprehensive system and mathematical specification for an automated Customer Lifetime Value (pCLV) estimation engine that assigns forward-looking net present value scores and churn probabilities to {{target_cohort}} to orchestrate {{campaign_interventions}}.

Method

1. Define RFM (Recency, Frequency, Monetary value) feature extraction schemas over {{transaction_history_window}}.
2. Specify the probability distribution assumptions for repeat transaction frequency (e.g., BG/NBD or Pareto/NBD).
3. Establish the conditional monetary value sub-model parameterization using Gamma-Gamma architectures based on {{margin_profiles}}.
4. Formalize the expected residual transactions and expected monetary value equations.
5. Incorporate {{discount_rate_assumptions}} into continuous-time discounted cash flow formulations.
6. Define dynamic threshold boundaries mapping predicted churn probability and residual CLV against {{churn_latency_threshold}}.
7. Specify the payload interface mapping calculated segments directly to {{campaign_interventions}}.

Constraints

• MUST define distributional assumptions and parameter convergence criteria for the sub-models.
• MUST explicitly show how gross margin from {{margin_profiles}} is applied to top-line monetary predictions.
• MUST NOT treat customer drop-out as a static rule-based flag; it must be probabilistically derived.
• Data definitions must strictly conform to transactional event schemas.

Output format

1. Data Schema & Feature Engineering

Input table requirements, RFM extraction logic, and time-slicing rules.

2. Statistical Sub-Model Architecture

Frequency/recency model, monetary model, and joint likelihood estimation formulas.

3. Net Present Value Scoring Formula

Integration of margin and discount rate logic for forward-looking cohort prediction.

4. Decision Rule & Integration Payload

Logic mapping CLV deciles and churn risk scores into lifecycle campaign triggers.

Self-review

• Ensure all 6 context variables are deeply integrated into the analytical framework.
• Confirm mathematical rigor for both transaction count and average spend calculations.
• Check that integration logic clearly connects math outputs to marketing intervention triggers.