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Forecasting The Pricing Kernel of IBNR Claims Development In Property-Casualty Insurance

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  • Cadogan, Godfrey

Abstract

A new method of forecasting the pricing kernel, i.e., stochastic claim inflation or link ratio function, of incurred but not reported (IBNR) claims (in property casualty insurance) from residuals in a dynamic claims forecast model is presented. We employ a pseudo Kalman filter approach by using claims risk exposure estimates to reconstruct innovations in stochastic claims development. Whereupon we find that the pricing kernel forecast is a product measure of the innovations. We show how these results impact performance measurement including but not limited to risk-adjusted return on capital by and through insurance accounting relationships for adjusted underwriting results; and loss ratio or pure premium calculations. Additionally, we show how, in the context of Wold decomposition, diagnostics from our model can be used to compute signal to noise ratio for, and cross check, unobservable pricing kernels used to forecast claims. Furthermore, we prove that a single risk exposure factor connects seemingly unrelated specifications for loss link ratio, and claims volatility.

Suggested Citation

  • Cadogan, Godfrey, 2010. "Forecasting The Pricing Kernel of IBNR Claims Development In Property-Casualty Insurance," MPRA Paper 23235, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:23235
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    References listed on IDEAS

    as
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    6. Taylor, G. C., 1977. "Separation of Inflation and other Effects from the Distribution of Non-Life Insurance Claim Delays," ASTIN Bulletin, Cambridge University Press, vol. 9(1-2), pages 219-230, January.
    7. Verrall, R. J., 2000. "An investigation into stochastic claims reserving models and the chain-ladder technique," Insurance: Mathematics and Economics, Elsevier, vol. 26(1), pages 91-99, February.
    8. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
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    More about this item

    Keywords

    IBNR claims ladder; claims reserve forecast; stochastic claim inflation; claims risk exposure; link ratio function; property-casualty insurance; insurance accounting;
    All these keywords.

    JEL classification:

    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
    • M49 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Accounting - - - Other

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