PROCEEDINGS May 15, 16, 17, 18, 2005 - Casualty Actuarial Society

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250 WHEN CAN ACCIDENT YEARS BE REGARDED AS DEVELOPMENT YEARS?A further important consequence of this property is that parametersin the two directions can take the roles of both a leveland a ratio.We know within ourselves that the two directions are fundamentallydifferent, both in general appearance of their trends andin spirit. The development year direction tends to have a smoothrun-off shape, where the incremental losses tend to increase initiallyto a peak somewhere in the first few developments andthen smoothly decrease in the tail, while the accident years tendto have quite a different pattern. Yet the model itself makes nosuch distinction–it does not contain important information wealready know about claims payments (i.e., the structure in lossdata).Indeed, the chain ladder model, being a two-way cross classificationmodel (as has been recognized by numerous authors),not only fails to distinguish between accident years and developmentyears, it ignores the relationships between years withineither category.Consider the two plots of logs of paid data against developmentyear in Figure 5. Can you tell which one is the real data?Most practitioners will instantly (and correctly) guess that thelower plot is the real one. We know that paid data often has astrong pattern to its runoff–that nearby development periodstend to be more alike than ones further away, and further, weusually observe smooth trends relating them.Clearly the accident and development labels mean something,and you can’t arbitrarily relabel them without affecting the informationin the data. The observations in development year 3 donot just tend to be closer to each other than to observations fromother columns, they also tend to be more like the observations indevelopment years 2 and 4 than they are like observations fromcolumns further away. In a two-way cross-classification model,we can arbitrarily rearrange the group labels within both factors,and even interchange the factors without changing the fit. If the
WHEN CAN ACCIDENT YEARS BE REGARDED AS DEVELOPMENT YEARS? 251FIGURE 5Plot of Exposure-Adjusted Log Paid Incremental DataAgainst Development Year (one of the plots has hadits development period labels randomly allocated)labels do carry information over and above being arbitrary identifiersof a category into which the observation falls (as they doin claims runoff), the chain ladder model is inappropriate.With the lower plot of Figure 5, one could omit all of thedata for any development period between 1 and 8 (i.e., replacethe observations with missing values) and still be able to get a
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VOLUME XCII NUMBERS 176 and 177PROC
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FOREWORDActuarial science originate
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2005 PROCEEDINGSCONTENTS OF VOLUME
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2005 PROCEEDINGSCONTENTS OF VOLUME
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Editorial Committee, Proceedings Ed
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10 AN EXAMINATION OF THE INFLUENCE
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AN EXAMINATION OF THE INFLUENCE OF
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RISKINESS LEVERAGE MODELSRODNEY KRE
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RISKINESS LEVERAGE MODELS 33There a
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RISKINESS LEVERAGE MODELS 35where f
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RISKINESS LEVERAGE MODELS 37where a
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RISKINESS LEVERAGE MODELS 39Various
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RISKINESS LEVERAGE MODELS 59APPENDI
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DISCUSSION OF A PAPER PRESENTED AT
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RISKINESS LEVERAGE MODELS 63known t
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RISKINESS LEVERAGE MODELS 65to be a
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RISKINESS LEVERAGE MODELS 67implies
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RISKINESS LEVERAGE MODELS 69bad res
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RISKINESS LEVERAGE MODELS 734. INTE
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RISKINESS LEVERAGE MODELS 79REFEREN
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RISKINESS LEVERAGE MODELS 81EXHIBIT
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RISKINESS LEVERAGE MODELS 83
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WHY LARGER RISKS HAVE SMALLER INSUR
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ADDRESS TO NEW MEMBERS 151ateship a
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ADDRESS TO NEW MEMBERS 153You shoul
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ADDRESS TO NEW MEMBERS 155strength
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MINUTES OF THE 2005 CAS SPRING MEET
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MINUTES OF THE 2005 SPRING MEETING
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Volume XCII, Part 2 No. 177PROCEEDI
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MODELING FINANCIAL SCENARIOS 179Bab
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Page 249 and 250: WHEN CAN ACCIDENT YEARS BE REGARDED
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Page 267 and 268: THE APPLICATION OF FUNDAMENTAL VALU
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THE APPLICATION OF FUNDAMENTAL VALU
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A NEW METHOD OF ESTIMATING LOSS RES
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ARCHITECTURE FOR RESIDENTIAL PROPER
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ESTIMATING THE WORKERS COMPENSATION
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INCORPORATION OF FIXED EXPENSESGEOF
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DISCUSSION OF PAPER PUBLISHED INVOL
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APPLICATION OF THE OPTION MARKET PA
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THE “MODIFIED BORNHUETTER-FERGUSO
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ADDRESS TO NEW MEMBERS-NOVEMBER 14,
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ADDRESS TO NEW MEMBERS 743Now to an
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PRESIDENTIAL ADDRESS-NOVEMBER 14, 2
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MINUTES OF THE 2005 CAS ANNUAL MEET
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MINUTES OF THE 2005 ANNUAL MEETING
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REPORT OF THE VICE PRESIDENT-ADMINI
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2005 EXAMINATIONS—SUCCESSFUL CAND
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OBITUARIESROBERT GRANT ESPIECLYDE H
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OBITUARIES 825SIDNEY M. HAMMER1931
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OBITUARIES 827J. GARY LaROSE1947—
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OBITUARIES 829PAUL J. SCHEEL SR.193
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OBITUARIES 831LEO M. STANKUSCirca 1
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INDEX TO VOLUME XCIIPage2005 EXAMIN
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835GRAVES, CLYDE H.INDEX—CONTINUE
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837INDEX—CONTINUEDREPORT OF THE V
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PROCEEDINGS May 15, 16, 17, 18, 2005 - Casualty Actuarial Society

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