Optimising customer equity through engagement

Customer lifetime value (CLV) is the discounted sum of future cash flows due to a relationship with a single customer and customer equity (CE) is the sum of CLVs from all current and future customers of a company. Maximising CE is a central goal for customer relationship management. This paper presents a framework to use Markov chain models to optimise CE, allowing for actions taken at the segment level such as new customer acquisition, retention, and win-back, and controlling for engagement. The framework is tailored for subscription services but applies more generally. We derive closed-form expressions for the finite horizon case and partial derivatives for sensitivity analysis. Finally, we give an empirical example illustrating sensitivity analysis and how optimisation using gradient descent can guide strategic decisions by estimating the optimal levels of the decision variables.