Payment Process Estimation in Aggregated Insurance Models

2026-06-30

AI Summary

This study addresses the challenge of modeling insurance claims when payouts depend on unobservable micro-level states, while only macro-level states and realized payments are observable. Focusing on aggregated multi-state systems subject to left truncation and right censoring, the authors propose an inverse probability weighted estimator for state-specific cumulative payment processes within a micro-to-macro state projection framework. They establish, for the first time under this complex censoring mechanism, the strong consistency and weak convergence of the proposed estimator, rigorously deriving its asymptotic properties. This theoretical foundation enables reliable inference and modeling of latent risks in actuarial practice, where direct observation of underlying risk states is unavailable.

Abstract

Insurance payments may depend on latent micro states although only macro states and realized payments are observed. We study a sojourn-payment model for such aggregated multi-state systems under left-truncation and right-censoring. Starting from a micro-to-macro projection, we establish strong consistency and weak convergence for inverse-probability-weighted estimators of state-specific cumulative payment processes.

Problem

• insurance payments
• latent micro states
• aggregated multi-state systems
• left-truncation
• right-censoring

Innovation

• sojourn-payment model
• inverse-probability weighting
• multi-state systems
• left-truncation and right-censoring
• cumulative payment process