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232033 (M42, E10) Chain ladder prediction and asset liability management
Abstract and Reviews 232031 (M40, M10) Techniques for the Conversion of Los Development Factors Spore L., Casualty Actuarial Socie~ Forum, Including the DFA Call Papers, Summer 1998 It sometimes happens that accident year development factors are available and policy year factors are not and vice versa. The purpose of this paper is to formulate a mathematical technique for converting from one form into another under various assumptions concerning the time during the calendar year that policies are written. The connection between the policy year factor and the influence of changing exposures on accident year development is then explored.
Keywords: Development factors, Policy year factors. M42: LOSS RESERVES (INCL. I.B.N.R)
232032 (M42, M10) Chain Ladder, Marginal Sum and Maximum Likelihood Estimation Schmidt K.D., Wiinsche A., Deutsche Gesellschafifiir Versicherungsmathematik, Band XXIII, Heft 3, April 1998. The chain ladder method is one of the most famous methods using in reserving. It exploits all data from the run-off triangle and provides simple estimates of the expected ultimate aggregate claims. Simplicity of an estimator is important for its application in practice, but its performance usually depends upon the stochastic mechanism generating the data. In the present paper the authors consider two stochastic models which reflect certain elementary ideas on the occurrence and the delay in reporting of claims. They show that in these models the chain ladder estimators of the expected ultimate aggregate claims result from classical statistical estimation principles.
Keywords: Chain ladder, Loss reserving. 232033 (M42, El0) Chain Ladder Prediction and Asset Liability Management Schmidt K.D., Dresdner Schrifien zur Versicherungs mathematik 2/1997 The chain ladder method is one of the most common methods of loss reserving. From the practical point of view, there are two arguments in favor of the chain ladder method: Then method is simple, and its exploits all data from the run-off triangle. These arguments, however, do not settle the question whether or not the chain ladder method is preferable to other methods
191
of loss reserving. The quality of the chain ladder method depends on the stochastic mechanism, or stochastic model, generating the data. In the present paper we consider the model of Schnaus. Under the assumptions of this model, we show that the family of all chain ladder predictors is, in a reasonable sense, superior to many other families of predictors. This result is of interest with regard to asset liability management.
Keywords: Chain laddeT, Asset liabili~ management. 232034 (M42, M10) The Application of Cumulative Distribution Functions in the Stochastic Chain Ladder Model Tu S.T., CasualS, Actuarial Soceity Forum, Including the DFA Call Papers, Summer 1998 A new Stochastic model based on the traditional chain ladder is introduced. It makes explicit use of cumulative distribution functions and payment patterns. It incorporates a mathematical rationale for non-stochastic variations in the age-to-age factors. Perturbation methods are used to obtain and justify the solution. Estimation of liabilities in the tail is a natural product of the model. All stochastic variables are assumed to be normally distributed, and the assumption is then confirmed with the chi square goodness-of-fit test. Extensive numerical solutions of an actual problem are given. Several new avenues of related research are suggested.
Keywords: Chain ladder, Loss reserving, Cumulative distribution functions, Tail factor, Stochastic models, Perturbation theo~'. M43: F L U C T U A T I O N RESERVES, SOLVENCY MARGINS 232035 (M43, M10) A Decomposition of Actuarial Surplus and Applications Dufresne D., Centre for Actuarial Studies, The Universi~, of Melbourne, Research paper nr. 49, Jonua~' 1998. The actuarial gain is the unexpected increase of the actuarial surplus over a certain period, usually one year (a loss is a negative gain). A Decomposition Theorem for the surplus in terms of past gains is derived. If actuarial assumptions are unbiased, then the arithmetic sum of the gains forms a martingle. The latter has qualitatively the same behavior as a zero-mean random walk. However, the process obtained by accumulating the gains with interest diverges to plus or minus infinity. Also considered are biased actuarial assumptions, and connections with Risk Theory. Mathematically, all this is closely related to the
Keywords: Development factors, Policy year factors. M42: LOSS RESERVES (INCL. I.B.N.R)
232032 (M42, M10) Chain Ladder, Marginal Sum and Maximum Likelihood Estimation Schmidt K.D., Wiinsche A., Deutsche Gesellschafifiir Versicherungsmathematik, Band XXIII, Heft 3, April 1998. The chain ladder method is one of the most famous methods using in reserving. It exploits all data from the run-off triangle and provides simple estimates of the expected ultimate aggregate claims. Simplicity of an estimator is important for its application in practice, but its performance usually depends upon the stochastic mechanism generating the data. In the present paper the authors consider two stochastic models which reflect certain elementary ideas on the occurrence and the delay in reporting of claims. They show that in these models the chain ladder estimators of the expected ultimate aggregate claims result from classical statistical estimation principles.
Keywords: Chain ladder, Loss reserving. 232033 (M42, El0) Chain Ladder Prediction and Asset Liability Management Schmidt K.D., Dresdner Schrifien zur Versicherungs mathematik 2/1997 The chain ladder method is one of the most common methods of loss reserving. From the practical point of view, there are two arguments in favor of the chain ladder method: Then method is simple, and its exploits all data from the run-off triangle. These arguments, however, do not settle the question whether or not the chain ladder method is preferable to other methods
191
of loss reserving. The quality of the chain ladder method depends on the stochastic mechanism, or stochastic model, generating the data. In the present paper we consider the model of Schnaus. Under the assumptions of this model, we show that the family of all chain ladder predictors is, in a reasonable sense, superior to many other families of predictors. This result is of interest with regard to asset liability management.
Keywords: Chain laddeT, Asset liabili~ management. 232034 (M42, M10) The Application of Cumulative Distribution Functions in the Stochastic Chain Ladder Model Tu S.T., CasualS, Actuarial Soceity Forum, Including the DFA Call Papers, Summer 1998 A new Stochastic model based on the traditional chain ladder is introduced. It makes explicit use of cumulative distribution functions and payment patterns. It incorporates a mathematical rationale for non-stochastic variations in the age-to-age factors. Perturbation methods are used to obtain and justify the solution. Estimation of liabilities in the tail is a natural product of the model. All stochastic variables are assumed to be normally distributed, and the assumption is then confirmed with the chi square goodness-of-fit test. Extensive numerical solutions of an actual problem are given. Several new avenues of related research are suggested.
Keywords: Chain ladder, Loss reserving, Cumulative distribution functions, Tail factor, Stochastic models, Perturbation theo~'. M43: F L U C T U A T I O N RESERVES, SOLVENCY MARGINS 232035 (M43, M10) A Decomposition of Actuarial Surplus and Applications Dufresne D., Centre for Actuarial Studies, The Universi~, of Melbourne, Research paper nr. 49, Jonua~' 1998. The actuarial gain is the unexpected increase of the actuarial surplus over a certain period, usually one year (a loss is a negative gain). A Decomposition Theorem for the surplus in terms of past gains is derived. If actuarial assumptions are unbiased, then the arithmetic sum of the gains forms a martingle. The latter has qualitatively the same behavior as a zero-mean random walk. However, the process obtained by accumulating the gains with interest diverges to plus or minus infinity. Also considered are biased actuarial assumptions, and connections with Risk Theory. Mathematically, all this is closely related to the