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Beyond the Actuarial Mean: A Stochastic, Multi-Layered Framework for Dynamic Ratemaking and Loss Reserving in Property and Casualty Insurance
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
[ L_i,j = \lambda_i \cdot \gamma_j \cdot \exp(\eta_i,j + \tau_i \cdot \theta_j) \cdot \nu_i,j ] [ L_i,j = \lambda_i \cdot \gamma_j \cdot \exp(\eta_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
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 ).
[ 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 :