Bootstrapping the triangles

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Chain ladder diagnosticsValue0e+00 2e+06 4e+06 6e+06Mack Chain Ladder ResultsForecast●Latest●●● ● ●●●●●1 2 3 4 5 6 7 8 9 10AmountChain ladder developments by origin period1e+06 3e+06 5e+06 7e+06223234434234 2 51 1611 127358 561723456 11123465789Standardised residuals−1 0 1 2●●●●●●● ●●● ●● ●● ●●●●●●●● ●●●●● ●●● ● ●●● ●●● ●●●●●1234567890●2 4 6 8 101e+06 2e+06 3e+06 4e+06 5e+06Origin periodDevelopment periodFittedStandardised residuals−1 0 1 2●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●Standardised residuals−1 0 1 2●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●Standardised residuals−1 0 1 2●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●2 4 6 8Origin period2 4 6 8Calendar period1 2 3 4 5 6 7 8Development period
Bootstrap resultsHistogram of Total.IBNRecdf(Total.IBNR)Frequency0 50 150 250Fn(x)0.0 0.4 0.81.0e+07 2.0e+07 3.0e+071.0e+07 2.0e+07 3.0e+07Total IBNRTotal IBNRultimate claims costs5.0e+06 1.5e+07●Simulated ultimate claims costMean ultimate claim●● ●●● ●● ●●●●●●●●●●●●●●●●●latest incremental claims0 1000000 2000000●Latest actual incremental claimsagainst simulated values● Latest actual●●●●●●●●●●●●●●●●●1 2 3 4 5 6 7 8 9 10origin period1 2 3 4 5 6 7 8 9 10origin period
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 30 and 31: Mack CL vs bootstrapGLM (ODP)Accide
Page 32 and 33: Conclusions- mean and variance do n
Page 34: Thank you !pesta@karlin.mff.cuni.cz

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