Transaction time models in multi-state life insurance

TL;DR

This paper introduces transaction time models for multi-state life insurance to better handle delays in state reporting, providing explicit formulas for reserves and linking to classic models.

Contribution

It develops a new class of transaction time models that incorporate reporting delays, extending classic multi-state models for real-time policy development.

Findings

Explicit expressions for transaction time reserves in disability coverage.

A theoretical link between transaction time and classic models.

Practical implications for insurance reserve calculations.

Abstract

In life insurance contracts, benefits and premiums are typically paid contingent on the biometric state of the insured. Due to delays between the occurrence, reporting, and settlement of changes to the biometric state, the state process is not fully observable in real-time. This fact implies that the classic multi-state models for the biometric state of the insured are not able to describe the development of the policy in real-time, which encompasses handling of incurred-but-not-reported and reported-but-not-settled claims. We give a fundamental treatment of the problem in the setting of continuous-time multi-state life insurance by introducing a new class of models: transaction time models. The relation between the transaction time model and the classic model is studied and a result linking the present values in the two models is derived. The results and their practical implications are illustrated for disability coverages, where we obtain explicit expressions for the transaction time reserve in specific models.