Dynamic Pricing and Contracting Strategies for Value-Based Care Agreements Informed by Advanced Predictive Modeling

Abstract

This paper develops a unified stochastic control and machine learning framework for designing dynamic pricing and contracting strategies in value-based care (VBC) agreements. We formulate the interaction between a payer and an integrated provider network as a continuous-time principal–agent problem under moral hazard, where the provider exerts treatment intensity controls that influence a multidimensional diffusion process representing patient health states and resource utilization metrics. The payer designs a reimbursement rate function that adapts to observed aggregate outcomes via parameter updates driven by Bayesian filtering of latent health trajectories. The provider’s optimal control is derived by solving the associated Hamilton–Jacobi–Bellman (HJB) equation with hidden actions, yielding a feedback law expressed in terms of the marginal value function gradients. To estimate unknown drift and diffusion functions and to forecast high-dimensional state trajectories, we integrate Gaussian process regression with deep recurrent neural networks within a variational inference framework. This hybrid predictive pipeline informs a stochastic gradient ascent algorithm for optimizing neural-network–parameterized pricing schedules under budget-neutrality and quality-of-care constraints. Numerical experiments on large synthetic cohorts demonstrate that dynamic pricing reduces expected cost by up to 15\% relative to static bundled payments while maintaining equivalent quality-adjusted life-year benchmarks. Sensitivity analyses reveal robustness to provider risk aversion and forecast error. The proposed methodology provides a rigorous, implementable foundation for data-driven VBC contracts that align financial incentives with patient-centered outcomes.