Logo PTI Logo FedCSIS

Position Papers of the 21st Conference on Computer Science and Intelligence Systems

Annals of Computer Science and Information Systems, Volume 48

Backtesting Split Frequency–Severity Models in Motor third-party liability (MTPL) Insurance Under Claims Inflation

, ,

DOI: http://dx.doi.org/10.15439/2026F3531

Citation: Ondřej Vít, ,

Full text

Abstract. Frequency--severity models in motor third-party liability (MTPL) insurance commonly partition claims into size buckets separated by a fixed monetary threshold. While this split improves model fit by allowing different distributional assumptions for small and large claims, it introduces a methodological challenge for backtesting: nominal claims inflation causes claims to migrate across the threshold boundary over time. We formalise the spillover effect that arises when an inflation-adjusted claim crosses from the small into the large bucket, and propose an additive decomposition of aggregate severity changes into a within-bucket inflation component and a cross-bucket migration component. We derive closed-form approximations under a lognormal severity assumption and validate the framework on a Czech MTPL portfolio spanning 2022--2025 with a threshold of 100 000 CZK. Our results show that ignoring the spillover effect overestimates large-claim frequency by 5--35\% depending on the assumed inflation rate, and that the cross-bucket migration component dominates the observed severity increase, accounting for 85--100\% of the total change. A sensitivity analysis across threshold levels and inflation rates demonstrates that the effect is robust and practically relevant for a wide range of model configurations.

References

  1. E. Ohlsson and B. Johansson, Non-Life Insurance Pricing with Generalized Linear Models. Berlin: Springer, 2010.
  2. M. Denuit, X. Maréchal, S. Pitrebois, and J.-F. Walhin, Actuarial Modelling of Claim Counts: Risk Classification, Credibility and BonusMalus Systems. Chichester: Wiley, 2007.
  3. S. A. Klugman, H. H. Panjer, and G. E. Willmot, Loss Models: From Data to Decisions, 5th ed. Hoboken, NJ: Wiley, 2019.
  4. T. Mikosch, Non-Life Insurance Mathematics: An Introduction with Stochastic Processes. Berlin: Springer, 2004.
  5. Czech Statistical Office, “Consumer price indices—time series,” 2025, available at https://www.czso.cz.
  6. P. Embrechts, C. Klüppelberg, and T. Mikosch, Modelling Extremal Events for Insurance and Finance. Berlin: Springer, 1997.
  7. H. Albrecher, J. Beirlant, and J. L. Teugels, Reinsurance: Actuarial and Statistical Aspects. Chichester: Wiley, 2017.
  8. M. V. Wüthrich and M. Merz, Stochastic Claims Reserving Methods in Insurance. Chichester: Wiley, 2008.
  9. G. Taylor, Loss Reserving: An Actuarial Perspective. Boston: Kluwer Academic, 2000.
  10. P. Parodi, “Triangle-free reserving: A non-traditional framework for estimating reserves and reserve uncertainty,” British Actuarial Journal, vol. 19, no. 1, pp. 168–218, 2014.
  11. Česká kancelář pojistitelů (Czech Insurers’ Bureau), https://www.ckp.cz, accessed 2025.
  12. M. Zukanović, A. Radosavčević, A. Poledica, P. Milošević, and I. Luković, “Evaluating effectiveness of nonlinear dimensionality reduction in hedge funds’ returns forecasting,” in Proc. 20th Conf. on Computer Science and Intelligence Systems (FedCSIS), ser. Annals of Computer Science and Information Systems, vol. 43. IEEE, 2025, pp. 411–416.