mCube: A multinomial micro-level reserving model

Emmanuel Jordy Menvouta; Robin Van Oirbeek; Tim Verdonck; Emmanuel Jordy Menvouta; Robin Van Oirbeek; Tim Verdonck

doi:10.3934/jimo.2026097

Journal of Industrial and Management Optimization

2026, Volume 22, Issue 6: 2647-2682. doi: 10.3934/jimo.2026097

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mCube: A multinomial micro-level reserving model

1.
KU Leuven, Department of Mathematics, Leuven, Belgium
2.
Allianz Benelux, Boulevard Roi Albert Ⅱ 32, Brussels, Belgium
3.
University of Antwerp – imec, Department of Mathematics, Antwerp, Belgium

Received: 19 December 2025 Revised: 08 April 2026 Accepted: 13 April 2026 Published: 13 May 2026
62P05

This paper presents a multinomial multi-state micro-level reserving model, denoted mCube. We propose a unified framework for modelling the time and the payment process for incurred but not reported (IBNR) and reported but not settled (RBNS) claims and for modeling IBNR claim counts. mCube is a hybrid reserving framework: IBNR counts are estimated at the macro level, while post-reporting claim development is modelled at the micro level. We use multinomial distributions for the time process and spliced mixture models for the payment process. We illustrate the strong performance of the proposed model on a real data set of a major insurance company consisting of bodily injury claims. In our application, the proposed model produces the best estimate distribution. In the case study on a real insurance portfolio, this distribution is approximately centered around the true reserve. A simulation study on synthetic data confirms meaningful claim-level predictive accuracy across multiple scenarios.
- individual claims,
- IBNR,
- RBNS,
- micro-level reserving,
- multinomial model
Citation: Emmanuel Jordy Menvouta, Robin Van Oirbeek, Tim Verdonck. mCube: A multinomial micro-level reserving model[J]. Journal of Industrial and Management Optimization, 2026, 22(6): 2647-2682. doi: 10.3934/jimo.2026097

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Abstract

This paper presents a multinomial multi-state micro-level reserving model, denoted mCube. We propose a unified framework for modelling the time and the payment process for incurred but not reported (IBNR) and reported but not settled (RBNS) claims and for modeling IBNR claim counts. mCube is a hybrid reserving framework: IBNR counts are estimated at the macro level, while post-reporting claim development is modelled at the micro level. We use multinomial distributions for the time process and spliced mixture models for the payment process. We illustrate the strong performance of the proposed model on a real data set of a major insurance company consisting of bodily injury claims. In our application, the proposed model produces the best estimate distribution. In the case study on a real insurance portfolio, this distribution is approximately centered around the true reserve. A simulation study on synthetic data confirms meaningful claim-level predictive accuracy across multiple scenarios.

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