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Transaction time models in multi-state life insurance

Author

Listed:
  • Kristian Buchardt
  • Christian Furrer
  • Oliver Lunding Sandqvist

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.

Suggested Citation

  • Kristian Buchardt & Christian Furrer & Oliver Lunding Sandqvist, 2022. "Transaction time models in multi-state life insurance," Papers 2209.06902, arXiv.org, revised Feb 2023.
    • Handle: RePEc:arx:papers:2209.06902
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    References listed on IDEAS

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    1. Crevecoeur, Jonas & Robben, Jens & Antonio, Katrien, 2022. "A hierarchical reserving model for reported non-life insurance claims," Insurance: Mathematics and Economics, Elsevier, vol. 104(C), pages 158-184.
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    Cited by:

    1. C. Furrer & O. L. Sandqvist, 2025. "Loss of earning capacity in Denmark -- an actuarial perspective," Papers 2501.11578, arXiv.org, revised Jun 2026.
    2. Catalina Lozano-Murcia & Francisco P. Romero & Jesus Serrano-Guerrero & Arturo Peralta & Jose A. Olivas, 2024. "Potential Applications of Explainable Artificial Intelligence to Actuarial Problems," Mathematics, MDPI, vol. 12(5), pages 1-13, February.
    3. Oliver Lunding Sandqvist, 2023. "A multistate approach to disability insurance reserving with information delays," Papers 2312.14324, arXiv.org, revised Jan 2025.

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