Bootstrapping the triangles

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Conclusions- mean and variance do not contain full informationabout the distribution cannot providequantities like VaR- assumption of log-normally distributed claims log-normally distributed reserves (far morerestrictive)- various types of residuals- bootstrap (simulated) distributionmimics the unknown distribution of reserves(a mathematical proof necessary)- R software provides a free sufficient actuarialenvironment for reserving
ReferencesEngland, P. D. and Verrall, R. J. (1999)Analytic and bootstrap estimates of predictionerrors in claims reserving.Insurance: Mathematics and Economics, 25.England, P. D. and Verrall, R. J. (2006)Predictive distributions of outstanding claims ingeneral insurance.Annals of Actuarial Science, 1 (2).Pesta, M. (2012)Total least squares and bootstrapping withapplication in calibration.Statistics: A Journal of Theoretical and AppliedStatistics.
Page 1 and 2: Bootstrapping the trianglesPrečo,
Page 3 and 4: Prologue forBootstrap- computationa
Page 5 and 6: Bootstrap- simple (distribution-ind
Page 7 and 8: Bootstrap example- input data (# of
Page 9 and 10: Run-off (incremental)triangleAccide
Page 11 and 12: Run-off (cumulative)triangleAcciden
Page 14 and 15: Raw residuals(R)r i,j = X i,j −
Page 16 and 17: Anscombe residuals I- in GLM or GEE
Page 18 and 19: Deviance residuals(D)r i,j = sign(X
Page 20 and 21: Adjusted residuals- alternative to
Page 22 and 23: Bootstrap procedure I- Ex: bootstra
Page 24 and 25: Bootstrap procedure III(7) calculat
Page 26 and 27: Development of claimsClaims1e+06 3e
Page 28 and 29: Chain ladder diagnosticsValue0e+00
Page 30 and 31: Mack CL vs bootstrapGLM (ODP)Accide
Page 34: Thank you !pesta@karlin.mff.cuni.cz

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