{"word_count": 816, "character_count": 6318}
Mercredi, on commence la modélisation du passif des compagnies d'assurance IARD. Plus particulièrement, nous parlerons des provisions pour sinistres à payer, ou “provision for claims outstanding (PCO)” selon la terminologie anglaise, i.e. “the estimated total cost of ultimate settlement of all claims incurred before the date of record, whether reported or not, less any amounts already paid out in respect thereof.” Je renvoie à la lecture de Le contrôle de la solvabilité des compagnies d’assurance  en ligne sur le site de l’OCDE, pour une vision globale des approches de ces provisions. La SOA avait publié un rapport en 2009, Comparison of Incurred But Not Reported IBNR Methods que j’encourage à lire.Le livre de référence sur le sujet est celui de Mario Wüthrich et Michael Merz. Les premiers chapitres (correspondant a ce qui sera vu en cours) peuvent être téléchargés sur http://actuaries.ch/…Nous aborderons mercredi les triangles. Parmi les triangles que nous manipulerons&#62; source("https://perso.univ-rennes1.fr/arthur.charpentier/bases.R")qui contient plusieurs fichiers, dont&#62; PAID     [,1] [,2] [,3] [,4] [,5] [,6][1,] 3209 4372 4411 4428 4435 4456[2,] 3367 4659 4696 4720 4730   NA[3,] 3871 5345 5338 5420   NA   NA[4,] 4239 5917 6020   NA   NA   NA[5,] 4929 6794   NA   NA   NA   NA[6,] 5217   NA   NA   NA   NA   NAainsi que le triangle évoqué sur http://rworkingparty.wikidot.com/&#62; OthLiabData = read.csv("http://www.casact.org/research/reserve_data/othliab_pos.csv",header=TRUE, sep=",")&#62; library(ChainLadder)&#62; OL = SumData=ddply(OthLiabData,.(AccidentYear,DevelopmentYear,DevelopmentLag),summarise,IncurLoss=sum(IncurLoss_h1-BulkLoss_h1),+ CumPaidLoss=sum(CumPaidLoss_h1), EarnedPremDIR=sum(EarnedPremDIR_h1))&#62; LossTri = as.triangle(OL, origin="AccidentYear",+ dev = "DevelopmentLag", value="IncurLoss")&#62; Year = as.triangle(OL, origin="AccidentYear",+ dev = "DevelopmentLag", value="DevelopmentYear")&#62; TRIANGLE=LossTri&#62; TRIANGLE[Year&#62;1997]=NA&#62; TRIANGLE      devorigin      1      2      3      4      5      6      7      8      9     10  1988 128747 195938 241180 283447 297402 308815 314126 317027 319135 319559  1989 135147 208767 270979 304488 330066 339871 344742 347800 353245     NA  1990 152400 238665 297495 348826 359413 364865 372436 372163     NA     NA  1991 151812 266245 357430 400405 423172 442329 460713     NA     NA     NA  1992 163737 269170 347469 381251 424810 451221     NA     NA     NA     NA  1993 187756 358573 431410 476674 504667     NA     NA     NA     NA     NA  1994 210590 351270 486947 581599     NA     NA     NA     NA     NA     NA  1995 213141 351363 444272     NA     NA     NA     NA     NA     NA     NA  1996 237162 378987     NA     NA     NA     NA     NA     NA     NA     NA  1997 220509     NA     NA     NA     NA     NA     NA     NA     NA     NALes transparents sont en ligne,Pour les lectures complémentaires, Best Estimates for Reserves de Glen Barnett et Ben Zehnwirth est téléchargeable sur http://casact.org/pubs/…. En 2004 , Ben Zehnwirth, Julie Sims et Mark Shapland ont publié Will Your Next Reserve Increase Be Your Last (en ligne sur http://contingencies.org/janfeb04/…) Lors des prochaines séances, nous aborderons les méthodes par simulations. J'encourage la lecture de about the bootstrap, http://insureware.com/Library/… Sinon, des compléments plus spécifiques sont téléchargeables,The Chain Ladder and Tweedie Distributed Claims Data par Greg TaylorChain-Ladder Bias: Its Reason and Meaning par Leigh Joseph HalliwellEstimating Predictive Distributions for Loss Reserve Models par Glenn MeyersUsing a Bayesian Approach for Claims Reserving par Mario WuthrichObtaining Predictive Distributions for Reserves Which Incorporate Expert Opinion par Richard VerrallLoss Reserve Estimates: A Statistical Approach for Determining “Reasonableness” par Mark ShaplandMunich Chain Ladder: A Reserving Method that Reduces the Gap between IBNR Projections Based on Paid Losses and IBNR Projections Based on Incurred Losses par Gerhard Quarg et Thomas MackThe Bornhuetter-Ferguson Principle par Klaus Schmidt et Mathias ZocherOn the Importance of Dispersion Modeling for Claims Reserving: An Application with the Tweedie Distribution par Jean-Philippe Boucher et Danail DavidovQuantifying Uncertainty in Reserve Estimates par Zia Rehman et Stuart KlugmanRobustifying Reserving par Gary Venter et Dumaria Rulina Tampubolon, voir aussi Robustifying ReservingBootstrap Estimation of the Predictive Distributions of Reserves Using Paid and Incurred Claims par Huijuan Liu et Richard VerrallPredictive Distributions for Reserves Which Separate True IBNR and IBNER Claims par Huijuan Liu et Richard VerrallThe Retrospective Testing of Stochastic Loss Reserve Models, par Glenn MeyersA GLM-Based Approach to Adjusting for Changes in Case Reserve Adequacy par Larry DeckerA Method for Modelling Varying Run-off Evolutions in Claims Reserving par Richard VerrallA Nonlinear Regression Model of Incurred But Not Reported Losses par Scott StelljesBack-Testing the ODP Bootstrap of the Paid Chain-Ladder Model with Actual Historical Claims Data par Jessica (Weng Kah) Leong, Shaun Wang et Han ChenA Practical Way to Estimate One-Year Reserve Risk par Ira RobbinClosed-Form Distribution of Prediction Uncertainty in Chain Ladder Reserving by Bayesian Approach par Ji YaoThe Prediction Error of Bornhuetter-Ferguson par Thomas MackStochastic Loss Reserving with the Collective Risk Model par Glenn MeyersOn the Accuracy of Loss Reserving Methodology par Tapio Boles et Andy StaudtBootstrapping Generalized Linear Models for Development Triangles Using Deviance Residuals par Thomas HartlFitting a GLM to Incomplete Development Triangles par Thomas HartlGauss—Markov Loss Prediction in a Linear Model par Alexander Ludwig et Klaus SchmidtAnatomy of Actuarial Methods of Loss Reserving par Prakash NarayanBootstrap Modeling: Beyond the Basics par Mark R. Shapland et Jessica (Weng Kah) LeongGLM Invariants par Fred KlinkerThe Retrospective Testing of Stochastic Loss Reserve Models par Glenn Meyers et Peng ShiA GLM-Based Approach to Adjusting for Changes in Case Reserve Adequacy par Larry DeckerTesting the Assumptions of Age-to-age Factors, par Gary Venter, voir aussi http://rationalargumentator.com/actuaryguide/…