A multistate approach to disability insurance reserving with information delays

TL;DR

The paper tackles disability insurance reserving in the presence of reporting and adjudication delays by embedding a continuous-time multistate framework within a two-layer model: a valid-time process that governs actual claim events and a transaction-time process that captures information arrival. Under conditional independence assumptions, the authors derive closed-form reserve expressions (CBNR, RBNS) that incorporate an IBNR-factor and adjudication probabilities, avoiding intensive Monte-Carlo simulation. Estimation uses a two-step approach aligned with prior work on reporting delays and adjudications, enabling parametric inference for hazards and delay distributions. A real-data application to the Danish LEC-DK19 dataset demonstrates noticeable differences from naive methods and highlights the practical value of accounting for information delays in disability-reserving. Overall, the framework provides a principled, implementable path to robust, interpretable reserves for long-duration disability cash flows affected by information delays.

Abstract

Disability insurance claims are often affected by lengthy reporting delays and adjudication processes. The classic multistate life insurance modeling framework is ill-suited to handle such information delays since the cash flow and available information can no longer be based on the biometric multistate process determining the contractual payments. We propose a new individual reserving model for disability insurance schemes which describes the claim evolution in real-time. Under suitable independence assumptions between the available information and the underlying biometric multistate process, we show that these new reserves may be calculated as natural modifications of the classic reserves. We propose suitable parametric estimators for the model constituents and a real data application shows the practical relevance of our concepts and results.

Figures (6)

• Figure 2.1: The state process $Y$ takes values in $\mathcal{J}=\{a,i_1,\dots,i_m,r,d\}$, being an illness-death model with $m$ disabled states $\mathcal{I}=\{i_1,\dots,i_m\}$ and a separate reactivated state. To reduce clutter, all transitions to and from $\mathcal{I}$ are illustrated as single dotted arrows. Transition between the disabled states is not possible.
• Figure 2.2: State space $\mathcal{J}^{(1)}$ for the process $Z^{(1)}$.
• Figure 2.3: Coarser state space for the process $Z^{(1)}$.
• Figure 5.1: The approximated portfolio level reserve decomposed by category.
• Figure B.1: Illustration of a run-off plot with origin at the end of the coverage period, where reserves consist of only IBNR and RBNS contributions.

Theorems & Definitions (25)

• Remark 2.1
• Remark 2.2
• Lemma 3.3
• Theorem 3.4
• proof
• Remark 3.5
• Remark 3.6
• Remark 3.7
• Theorem 3.8
• proof