A Hoerl-Type State-Space Model for Dynamic Reserving: Applications to Reporting Delays in Epidemiology

Reporting delays are a common challenge in actuarial reserving and infectious disease surveillance, where incomplete development information can distort real-time estimation and decision-making. Classical reserving methods, such as the chain ladder method, assume stable development patterns across event periods, which may be unrealistic when reporting behavior evolves over time. This paper develops a Hoerl-type state-space framework, in which development dynamics evolve as latent stochastic processes within a linear Gaussian state-space model. Estimation is conducted using the Kalman filter and Rauch-Tung-Striebel smoother, allowing recursive estimation under incomplete run-off triangles. The paper further establishes consistency and asymptotic normality for estimators of latent states, ultimate quantities, and the effective reproduction number. Simulation and empirical applications show that the proposed method performs comparably to Mack’s model under stable development patterns while providing substantially more accurate estimates of effective reproduction numbers when reporting behavior varies over time or delays remain unresolved near the boundary of the observation window. These results suggest that the proposed approach provides a flexible and theoretically grounded extension of classical actuarial reserving methods.