Cadogan, Godfrey (2010): Forecasting The Pricing Kernel of IBNR Claims Development In Property-Casualty Insurance.
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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.
|Item Type:||MPRA Paper|
|Original Title:||Forecasting The Pricing Kernel of IBNR Claims Development In Property-Casualty Insurance|
|Keywords:||IBNR claims ladder; claims reserve forecast; stochastic claim inflation; claims risk exposure; link ratio function; property-casualty insurance; insurance accounting|
|Subjects:||C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C53 - Forecasting and Prediction Methods; Simulation Methods
G - Financial Economics > G2 - Financial Institutions and Services > G22 - Insurance; Insurance Companies
M - Business Administration and Business Economics; Marketing; Accounting > M4 - Accounting and Auditing > M49 - Other
|Depositing User:||godfrey cadogan|
|Date Deposited:||12. Jun 2010 11:33|
|Last Modified:||13. Feb 2013 17:50|
Bardis, E. T., A. Majidi, and D. M. Murphy (2008). Manually Adjustable Link Ratio Model For Reserving. Casualty Actuarial Society E-Forum, 1–15.
Beaver, W. H., M. F. Mc Nichols, and K. K. Nelson (2003). Management of theLoss Reserve Accrual and the Distribution of Earnings in the Property-Casualty Insurance Industry. Journal of Accounting and Economics 35, 347–376.
Behncke, H. (2000). Insurance Mathematics: A European Model, mimeo. Universit¨at Osnabr¨uck - Institut f¨ur Mathematik, Germany; available at ftp://ftp.mathematik.uni-osnabrueck.de/pub/osm/versicher.ps.gz.
Bollerslev, T. (1986). Generalized Autoregressive Conditional Heteroskedasticity. Journal of Econometrics 31, 307–327.
Box, G. E. P., G. M. Jenkins, , and G. Riensel (1994). Time Series Forecasting and Control (3rd ed.). New Jersey: Prentice-Hall, Inc.
Brockwell, P. J. and R. A. Davis (1987). Time Series: Theory and Methods. New York, NY: Springer-Verlag.
Calandro, J. and T. J. O‘Brein (2004). A User Friendly Introduction to Property and Casualty Claim Reserves. Risk Management and Insurance Review 7(2), 177–187.
Campbell, J. Y., A. W. Lo, and A. C. MacKinlay (1997). The Econometrics of Financial Markets. Princeton, N. J.: Princeton University Press.
Davidson, R. and J. G. MacKinnon (2004). Econometric Theory and Methods. New York: Oxford Univ. Press.
De Jong, P. (2006). Forecasting Runoff Triangles. North American Actuarial Journal 10(2), 28–38.
Durrett, R. (2005). Probability: Theory and Examples (3rd ed.). Belmont, CA: Thompson Brooks-Cole.
Engle, R. (1982, July). Autoregressive Conditional heteroskedasticity with Estimatesof the Variance of United Kingdom Inflation. Econometrica 50(4), 987–10 08.
Engle, R. F. (2001). GARCH101: The Use of ARCH/GARCH Models in Applied Econometrics. Journal of Economic Perspectives 15(4), 157–168.
Engle, R. F. (2004). Risk and Volatility: Econometric Models and Financial Practice. Amer. Econ. Rev. 94(3), 405–420.
Gikhman, I. I. and A. V. Skorokhod (1969). Introduction to The Theory of Random Processes (Dover reprint 1996 ed.). Philadelphia, PA: W. B. Saunders.
Graham, J. R. and C. Harvey (2001). The Theory and Practice of Corporate Finance: Evidence From The Field. Journal of Financial Economics 60, 187–243.
Kremer, E. (1999, Oct.). Stochastic Claim Inflation in IBNR. presented at ASTIN Colloquium 1998, Glasgow, Scotland; published in Blatter der DGVFM 24(2):231-238.
K¨uppelberg, C. and M. Severin (2001). Prediction of Outstanding Claims. Institute of Statistics, Ludwig-Maximilians University in Munich, Paper No. 258, available at http://epub.ub.uni-muenchen.de/
Mack, T. (1994). Measuring The Variability of Chain Ladder Reserve Estimates. Casualty Actuarial Society Forum 1(1), 101–83.
Mills, T. C. and T. N. Markellos (2008). The Econometric Modeling of Financial Time Series (3rd ed.). New York: Cambridge University Press.
Nelson, K. K. (2000, Jan.). Rate Regulation, Competition, and Loss Reserve Discounting by Property-Casualty Insurers. Accounting Review 75(1), 115–138.
Shapland, M. R. (2007). Loss Reserve Estimation: A Statistical Approach for Determining Reasonableness. Variance:Advancing The Science of Risk 1(1), 120–148.
Shephard, N. (1996). Time Series Models in Econometrics, Finance and Other Fields, Chapter Statistical Aspects of ARCH and Stochastic Volatility, pp. 1– 67. London: Chapman & Hall.
Taylor, G. (1977). Separation of Inflation and Other Effects From the Distribution of Non-life Insurance Claim Delays. Astin Bulletin 9, 219–230.
Taylor, G. C. and F. R. Ashe (1983). Second Moments of Estimates of Outstanding Claims. Journal of Econometrics 23(1):37 – 61.
Verrall, R. J. (2000). An Investigation Into Stochastic Claims Reserving Models and The Claims Ladder Technique. Insurance, Mathematics and Economics 26, 91–98.
Ward, L. S. and D. H. Lee (2002). Practical Application of the Risk-Adjusted Return on Capital Framework. CAS Forum Summer 2002, Dynamic Financial Analysis, available at http://www.casact.org/pubs/forum/02sforum/02sf079.pdf
Wilkie, A. D. (1995). More On A Stochastic Asset Model For Actuarial Use. British Actuarial Journal 1(5), 777–964.
Wright, T. S. (1990). A Stochastic Method for Claims Reserving in General Insurance. Journal of Institute of Actuaries 117, 677–731.