A dual-LSTM model for CLV distributions: Diverging paths and bimodalities

Abstract

Abstract Virtually all customer lifetime value (CLV) models reduce the future of a customer to a single number, its expected value, implicitly assuming managers are indifferent to how that value materializes. Yet in a survey of management consultants from a leading global strategy firm, 79% would distinguish between two customers with identical expected CLV but different distributional profiles. This paper argues for a distributional view of CLV and develops a dual-LSTM framework: two interacting long short-term memory networks that jointly predict customer behavior and firm marketing strategy. Because customer responses and firm actions co-evolve dynamically through Monte Carlo simulation, the model generates rich CLV distributions that capture self-fulfilling prophecies, diverging loyalty paths, and bimodal outcomes that traditional approaches cannot structurally anticipate. Calibrated on nine years of individual-level data from 21,939 donors, the dual-LSTM consistently outperforms six benchmarks (including the Pareto/NBD, hierarchical Bayesian extensions, and state-of-the-art deep learning alternatives) on 19 of 24 evaluation metrics. Ranking customers by the right tail of their CLV distribution, rather than by expected CLV, improves targeting lift by up to 8.3%. Most critically, bimodal customers identified by the dual-LSTM—those at a fork in their customer journey—are significantly more responsive to marketing solicitations than observably identical unimodal customers (ROI of an additional solicitation at + 77% vs. -50%), a finding no other benchmark model replicates. These results demonstrate that CLV distributions are both estimable and actionable, enabling firms to allocate resources where marketing interventions yield the greatest marginal impact.