Technical reserving in non-life insurance : A literature review of aggregated and individual methods.
Mots-clés :
Reserves, Chain Ladder, Mack model, Run-off triangles, individual reserving, machine learning.Résumé
Estimating reserves in non-life insurance involves assessing the risks the insured faces and determining the amount of actuarial reserves needed to cover those risks. To estimate reserves, actuaries often use various methods, the most popular of which are deterministic methods, such as the Chain Ladder, and stochastic methods, such as the Mack model. These latter use simple statistical models considering the insured's historical data to estimate future losses. They basically rely on Run-off triangles of aggregated data by year of occurrence and development year. However, this aggregation often leads to a loss of relevant information. A powerful alternative could be Individual reserving, which incorporates information about the claims experience and policyholders’ individual characteristics through machine learning algorithms. This article reviews the various actuarial literature on reserve estimation in non-life insurance.
Références
E. Astesan, Les réserves techniques des sociétés d'assurances contre les accidents d'automobiles, Librairie générale de droit et de jurisprudence, 1938.
M. Thomas, «Measuring the variability of chain ladder reserve estimates, Spring, Vol 1,» Casualty Actuarial Society E-Forum, pp. 101-182, 1993.
M. Denuit et A. Charpentier, Mathématiques de l'assurance non-vie , Tome 1, Economica, 2004.
P. England et R. Verrall, «A FLEXIBLE FRAMEWORK FOR STOCHASTIC CLAIMS,» casualty actuarial society, pp. 1-38, 2001.
G. Quarg et T. Mack, «Munich Chain Ladder: A Reserving Method that Reduces the Gap between IBNR Projections Based on Paid Losses and IBNR Projections Based on Incurred Losses,» Blätter der Deutschen Gesellschaft für Versicherungs- und Finanzmathematik, vol. 26, n° %14, p. 597—630, 2004.
M. Braun, «The Impact of Regret on the Demand for Insurance,» Journal of Risk and Insurance, pp. 737-767, 2004.
C. Prohl, Schmidt et Klaus, «Multivariate Chain–Ladder,» pp. 1-14, 2005.
B.Verdier et A. Klinger, «JAB Chain Long-tail claims development,» ASTIN, 2005.
K. T. Hess, K. D. Schmidt et M. Zocher, «Multivariate loss prediction in the multivariate additive model,» Insurance: Mathematics and Economics, pp. 185-191, 2006.
H. Liu et R. Verrall, «Bootstrap Estimation of the Predictive Distributions of Reserves Using Paid and Incurred Claims,» CASUALTY ACTUARIAL SOCIETY, VOLUME 4/ISSUE 2, pp. 121-135, 2008.
M. Merz et M. Wüthrich, «Modelling The Claims Development Result,» Casualty Actuarial Society E-Forum, Fall 2008, pp. 542-568, 2008.
Verdonck et Debruyne, «The influence of individual claims on the chain-ladder estimates: Analysis and diagnostic tool,» Insurance: Mathematics and Economics, pp. 85-98, 2011.
R. Verrall et J. P. Nielsen, «Prediction of RBNS and IBNR claims using claim amounts and claim counts,» 10.2143/AST.40.2.2061139, 2010.
M. D. Martínez Miranda, B. Nielsen, J. P. Nielsen et R. Verrall, «Cash flow simulation for a model of outstanding liabilities based on claim amounts and claim numbers,» ASTIN Bulletin, pp. 107-129, 2011.
T. Mack, «The standard error of Chain Ladder reserve estimates: recursive calculation and inclusion of a tail factor,» Astin Bulletin, p. 361–366, 1999.
F. El kassimi et J. Zahi, «Health insurance pricing using CART decision trees algorithm,» International Journal of Computer Engineering and Data Science, Volume 2–Issue 3, pp. 5-9, 2022.
F. El kassimi et J. Zahi, «Proposition d’un modèle de tarification en assurance maladie obligatoire à travers le Modèle Linéaire Généralisé,» Alternatives Managériales Economiques, Vol. 4, No 4, pp. 462-481, 2022.
A. Renshaw et R. Verrall, «A Stochastic Model Underlying the Chain-Ladder Technique,» British Actuarial Journal, vol. 4, issue 4, , pp. 903-923, 1998.
T. Mack, «Distribution-free Calculation of the Standard Error of Chain Ladder Reserve Estimates,» ASTIN Bulletin, 23, pp. 213 - 225, 1993.
J. Zhou et J. Garrido, «A loss reserving method based on generalized linear models,» Society of Actuaries, 2009.
G. A. Spedicato, G. P. C. ACAS et S. Florian, «The Use of GAMLSS in Assessing the Distribution of Unpaid Claims Reserves.,» Arlington: Casualty Actuarial Society E-Forum, vol. 2., pp. 1-15, 2014.
H. Lopes, j. Barcellos, J. Kubrusly et C. Fernandes, «A non-parametric method for incurred but not reported claim reserve estimation,» International Journal for Uncertainty Quantification Volume 2, Issue 1, pp. 39-51, 2012.
P. Mulquiney, «Artificial Neural Networks in Insurance Loss Reserving,» JCIS, 2006.
M. Wuthrich, «Machine Learning in Individual Claims Reserving,» Swiss Finance Institute Research Paper, pp. 16-67, 2016.
M. Pigeon et F. Duval, «Individual Loss Reserving Using a Gradient Boosting-Based Approach,» Risks, 2019.
M. Wuthrich, «Machine learning in individual claims reserving,» SCANDINAVIAN ACTUARIAL JOURNAL, p. 465–480, 2018.
M. Baudry et C. Robert, «A machine learning approach for individual claims reserving in insurance,» WILEY, pp. 1-29, 2019.
A. Gabrielli, «A NEURAL NETWORK BOOSTED DOUBLE OVERDISPERSED POISSON CLAIMS RESERVING MODEL,» Cambridge University Press, pp. 25-60, 2019.
K. Kevin, «Individual claims forecasting with Bayesian mixture density networks,» Kasa AI, 2020.
O. Lopez, X. Milhaud et P. Thérond, « A TREE-BASED ALGORITHM ADAPTED TO MICROLEVEL RESERVING AND LONG DEVELOPMENT CLAIMS,» ASTIN Bulletin, pp. 741-762, 2019.
O. Lopez et X. Milhaud, «Individual reserving and nonparametric estimation of claim amounts subject to large reporting delays,» Scandinavian Actuarial Journal, pp. 34-53, 2020.
M. De Felice et F. Moriconi, «Claim Watching and Individual Claims Reserving Using Classification and Regression Trees,» Risks , pp. 1-36, 2019.
Friedman, Jerome, H. Trevor et R. Tibshirani., «The Elements of Statistical Learning,» Springer Series in Statistics, vol. 1., 2001.
F. Duval et M. Pigeon, «Individual loss reserving using a gradient boosting-based approach.,» Risks, 7(3),, 2019.
