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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.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 23235.

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Date of creation: 10 Jun 2010
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Handle: RePEc:pra:mprapa:23235

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Keywords: IBNR claims ladder; claims reserve forecast; stochastic claim inflation; claims risk exposure; link ratio function; property-casualty insurance; insurance accounting;

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  1. Taylor, G. C. & Ashe, F. R., 1983. "Second moments of estimates of outstanding claims," Journal of Econometrics, Elsevier, Elsevier, vol. 23(1), pages 37-61, September.
  2. Graham, John R. & Harvey, Campbell R., 2001. "The theory and practice of corporate finance: evidence from the field," Journal of Financial Economics, Elsevier, Elsevier, vol. 60(2-3), pages 187-243, May.
  3. Engle III, Robert F., 2003. "Risk and Volatility: Econometric Models and Financial Practice," Nobel Prize in Economics documents, Nobel Prize Committee 2003-4, Nobel Prize Committee.
  4. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
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