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Model Error (or Ambiguity) and Its Estimation, with Particular Application to Loss Reserving

Author

Listed:
  • Greg Taylor

    (School of Risk and Actuarial Studies, University of New South Wales, Randwick, NSW 2052, Australia)

  • Gráinne McGuire

    (Taylor Fry, 45 Clarence Street, Sydney, NSW 2000, Australia)

Abstract

This paper is concerned with the estimation of forecast error, particularly in relation to insurance loss reserving. Forecast error is generally regarded as consisting of three components, namely parameter, process and model errors. The first two of these components, and their estimation, are well understood, but less so model error. Model error itself is considered in two parts: one part that is capable of estimation from past data (internal model error), and another part that is not (external model error). Attention is focused here on internal model error. Estimation of this error component is approached by means of Bayesian model averaging, using the Bayesian interpretation of the LASSO. This is used to generate a set of admissible models, each with its prior probability and likelihood of observed data. A posterior on the model set, conditional on the data, may then be calculated. An estimate of model error (for a loss reserve estimate) is obtained as the variance of the loss reserve according to this posterior. The population of models entering materially into the support of the posterior may turn out to be “thinner” than desired, and bootstrapping of the LASSO is used to increase this population. This also provides the bonus of an estimate of parameter error. It turns out that the estimates of parameter and model errors are entangled, and dissociation of them is at least difficult, and possibly not even meaningful. These matters are discussed. The majority of the discussion applies to forecasting generally, but numerical illustration of the concepts is given in relation to insurance data and the problem of insurance loss reserving.

Suggested Citation

  • Greg Taylor & Gráinne McGuire, 2023. "Model Error (or Ambiguity) and Its Estimation, with Particular Application to Loss Reserving," Risks, MDPI, vol. 11(11), pages 1-28, October.
    • Handle: RePEc:gam:jrisks:v:11:y:2023:i:11:p:185-:d:1267129
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    References listed on IDEAS

    as
    1. Benjamin Avanzi & Mark Lavender & Greg Taylor & Bernard Wong, 2022. "On the impact of outliers in loss reserving," Papers 2203.00184, arXiv.org, revised Jun 2023.
    2. England, P.D. & Verrall, R.J., 2002. "Stochastic Claims Reserving in General Insurance," British Actuarial Journal, Cambridge University Press, vol. 8(3), pages 443-518, August.
    3. Yanwei Zhang & Vanja Dukic, 2013. "Predicting Multivariate Insurance Loss Payments Under the Bayesian Copula Framework," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 80(4), pages 891-919, December.
    4. Taylor, G. C., 1985. "Combination of estimates of outstanding claims in non-life insurance," Insurance: Mathematics and Economics, Elsevier, vol. 4(2), pages 81-91, April.
    5. Dahms, René, 2018. "Chain-Ladder Method And Midyear Loss Reserving," ASTIN Bulletin, Cambridge University Press, vol. 48(1), pages 3-24, January.
    6. Schneider, Judith C. & Schweizer, Nikolaus, 2015. "Robust measurement of (heavy-tailed) risks: Theory and implementation," Journal of Economic Dynamics and Control, Elsevier, vol. 61(C), pages 183-203.
    7. Taylor, G. C. & Ashe, F. R., 1983. "Second moments of estimates of outstanding claims," Journal of Econometrics, Elsevier, vol. 23(1), pages 37-61, September.
    Full references (including those not matched with items on IDEAS)

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