Estimation for multistate models subject to reporting delays and incomplete event adjudication with application to disability insurance

• Main Authors: Buchardt, K, Furrer, C, Sandqvist, O. L
• Format: Journal Article
• Language: English
• Published: 08.08.2025
• Subjects: Mathematics - Statistics Theory; Statistics - Methodology; Statistics - Theory
• DOI: 10.48550/arxiv.2311.04318

Accurate forecasting of an insurer's outstanding liabilities is vital for the solvency of insurance companies and the financial stability of the insurance sector. For health and disability insurance, the liabilities are intimately linked with the biometric event history of the insured. Complete observation of event histories is often impossible due to sampling effects such as right-censoring and left-truncation, but also due to reporting delays and incomplete event adjudication. In this paper, we develop a parametric two-step M-estimation method that takes the aforementioned effects into account, treating the latter two as partially exogenous. The approach is valid under weak assumptions and allows for complicated dependencies between the event history, reporting delays, and adjudication while remaining relatively simple to implement. The estimation approach has desirable properties which are demonstrated by theoretical results and numerical experiments. In the application, we introduce and consider a large portfolio of disability insurance policies. We find that properly accounting for the sampling effects has a large impact on the number of disabilities and reactivations that an insurer would forecast, allowing for a more accurate assessment of the insurer's liabilities and improved risk management.