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Thefollowing theorem makes itclear that (1) and (2) are indeed theimplicit assumptions of the chain ladder method. Theorem 1: Let D = {Cikli+k _< I+ 1} be the set of all data observed Under the assumptions (1) and (2) we have. E(CiiID) = Ci,t+ i- if1+ i -i'''" "fl- I". Proof: We use the abbreviation. El(X) = E(X~Cil,..., Ci, i+l-i).
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May 13, 2019 · On the other hand, it is well-known that chain ladder reserve estimates for the most recent accident years are very sensitive to variations in the data observed. Moreover, in recent years many other claims reserving procedures have been proposed and the results of all these procedures vary widely and also differ more or less from the chain ladder result.
362 THOMAS MACK are arbitrary weights which can be used by the actuary to downweight any outlying Fik. Normally, Wik = I for all i, k.
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The Institute of Actuaries of Australia Level 7 Challis House 4 Martin Place Sydney NSW Australia 2000 Telephone: +61 2 9233 3466 Facsimile: +61 2 9233 3446 Email: insact@actuaries.asn.au Website: www.actuaries.asn.au.
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Repeated applicatio of thn basie c chain ladder assumptio (1) andn of the above variance assumptio (3 yield)n s for th firste term of mse (R,) Var (C a \D) = Var,.
Mack [1] derived formulas for the chain ladder reserve risk when the age-to-age factors are based on the all-year weighted average. Murphy [4] derived recursive formulas for the chain ladder reserve risk under assumptions that are equivalent to Mack’s. The authors’ formulas yield different results, for reasons to be discussed herein.
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The Mack-Method. Is a textbook example of a proper statistical model with precise model assumptions and estimators. Through model-assumptions we will “re-invent” both methods. In the Mack-Method, both procedures are extended to include variability estimates. Recall the graphical interpretations.
