[ L_i,j = \lambda_i \cdot \gamma_j \cdot \exp(\eta_i,j + \tau_i \cdot \theta_j) \cdot \nu_i,j ]
We propose a :
Beyond the Actuarial Mean: A Stochastic, Multi-Layered Framework for Dynamic Ratemaking and Loss Reserving in Property and Casualty Insurance [ L_i,j = \lambda_i \cdot \gamma_j \cdot \exp(\eta_i,j
Loss reserving and ratemaking are two views of the same stochastic process—the full claims lifecycle. This paper proposes a deep integration via a Bayesian hierarchical model. 2. Theoretical Foundations: A Unified Loss Generation Model Let ( L_i,j ) be the incremental paid loss for accident year ( i ) and development year ( j ). Traditional reserving models ( L_i,j = \alpha_i \beta_j + \epsilon_i,j ). Ratemaking models the premium ( P_i ) as a function of exposure ( E_i ) and expected ultimate loss ( \hatU i ), where ( \hatU i = \sum j=0^J \hatL i,j ). Theoretical Foundations: A Unified Loss Generation Model Let
