Data Analytics for Non-Life Insurance Pricing

These notes aim at giving a broad skill set to the actuarial profession in non-life insurance pricing and data science. We start from the classical world of generalized linear models, generalized additive models and credibility theory. These methods form the basis of the deeper statistical understanding. We then present several machine learning techniques such as regression trees, bagging, random forest, boosting and support vector machines. Finally, we provide methodologies for analyzing telematic car driving data.

[1]  Hong Huo,et al.  Characterization of vehicle driving patterns and development of driving cycles in Chinese cities , 2008 .

[2]  Esbjörn Ohlsson,et al.  Non-Life Insurance Pricing with Generalized Linear Models , 2010 .

[3]  Tariq Muneer,et al.  The measurement of vehicular driving cycle within the city of Edinburgh. , 2001 .

[4]  Galit Shmueli,et al.  To Explain or To Predict? , 2010, 1101.0891.

[5]  Greg Ridgeway,et al.  Generalized Boosted Models: A guide to the gbm package , 2006 .

[6]  Yoav Freund,et al.  Boosting a weak learning algorithm by majority , 1990, COLT '90.

[7]  T. Therneau,et al.  An Introduction to Recursive Partitioning Using the RPART Routines , 2015 .

[8]  Mario V. Wuthrich,et al.  Insights from Inside Neural Networks , 2020 .

[9]  Guangyuan Gao,et al.  Feature extraction from telematics car driving heatmaps , 2018, European Actuarial Journal.

[10]  V. Tikhomirov On the Representation of Continuous Functions of Several Variables as Superpositions of Continuous Functions of one Variable and Addition , 1991 .

[11]  Gerda Claeskens,et al.  Unravelling the predictive power of telematics data in car insurance pricing , 2017 .

[12]  Pavel V. Shevchenko,et al.  Machine learning techniques for mortality modeling , 2017 .

[13]  Andrea Gabrielli,et al.  Neural network embedding of the over-dispersed Poisson reserving model , 2020 .

[14]  Trevor Hastie,et al.  Statistical Learning with Sparsity: The Lasso and Generalizations , 2015 .

[15]  J. Norris Appendix: probability and measure , 1997 .

[16]  J. Friedman Greedy function approximation: A gradient boosting machine. , 2001 .

[17]  Mario V. Wüthrich Machine learning in individual claims reserving , 2016 .

[18]  Alan Y. Chiang,et al.  Generalized Additive Models: An Introduction With R , 2007, Technometrics.

[19]  P. Petrushev Approximation by ridge functions and neural networks , 1999 .

[20]  Christian P. Robert,et al.  The Bayesian choice , 1994 .

[21]  A. Gelman,et al.  Weak convergence and optimal scaling of random walk Metropolis algorithms , 1997 .

[22]  Geoffrey E. Hinton,et al.  Bayesian Learning for Neural Networks , 1995 .

[23]  Jooyoung Park,et al.  Approximation and Radial-Basis-Function Networks , 1993, Neural Computation.

[24]  Giampiero Marra,et al.  Practical variable selection for generalized additive models , 2011, Comput. Stat. Data Anal..

[25]  Stefan M. Rüger,et al.  The Metric Structure of Weight Space , 1997, Neural Processing Letters.

[26]  Leslie G. Valiant,et al.  Cryptographic Limitations on Learning Boolean Formulae and Finite Automata , 1993, Machine Learning: From Theory to Applications.

[27]  F. Opitz Information geometry and its applications , 2012, 2012 9th European Radar Conference.

[28]  T. Zaslavsky Facing Up to Arrangements: Face-Count Formulas for Partitions of Space by Hyperplanes , 1975 .

[29]  K. Schittkowski,et al.  NONLINEAR PROGRAMMING , 2022 .

[30]  C. P. Lee,et al.  Development of a practical driving cycle construction methodology: A case study in Hong Kong , 2007 .

[31]  Peter Green,et al.  Markov chain Monte Carlo in Practice , 1996 .

[32]  Guigang Zhang,et al.  Deep Learning , 2016, Int. J. Semantic Comput..

[33]  Jimmy Ba,et al.  Adam: A Method for Stochastic Optimization , 2014, ICLR.

[34]  Nitish Srivastava,et al.  Dropout: a simple way to prevent neural networks from overfitting , 2014, J. Mach. Learn. Res..

[35]  Leo Breiman,et al.  Random Forests , 2001, Machine Learning.

[36]  Jooyoung Park,et al.  Universal Approximation Using Radial-Basis-Function Networks , 1991, Neural Computation.

[37]  S. Duane,et al.  Hybrid Monte Carlo , 1987 .

[38]  Michel Denuit,et al.  Multivariate credibility modelling for usage-based motor insurance pricing with behavioural data , 2019, Annals of Actuarial Science.

[39]  Leo Breiman,et al.  Statistical Modeling: The Two Cultures (with comments and a rejoinder by the author) , 2001, Statistical Science.

[40]  Jürg Schelldorfer,et al.  Nesting Classical Actuarial Models into Neural Networks , 2019, SSRN Electronic Journal.

[41]  P. Green Reversible jump Markov chain Monte Carlo computation and Bayesian model determination , 1995 .

[42]  Daniela M. Witten,et al.  An Introduction to Statistical Learning: with Applications in R , 2013 .

[43]  Jan Jung,et al.  On automobile insurance ratemaking , 1968, ASTIN Bulletin.

[44]  Andrew Gelman,et al.  The No-U-turn sampler: adaptively setting path lengths in Hamiltonian Monte Carlo , 2011, J. Mach. Learn. Res..

[45]  E. L. Lehmann,et al.  Theory of point estimation , 1950 .

[46]  Mario V. Wüthrich,et al.  Bias regularization in neural network models for general insurance pricing , 2019, European Actuarial Journal.

[47]  P. Green,et al.  Trans-dimensional Markov chain Monte Carlo , 2000 .

[48]  Montserrat Guillén,et al.  Telematics and Gender Discrimination: Some Usage-Based Evidence on Whether Men’s Risk of Accidents Differs from Women’s , 2016 .

[49]  Alexander Noll,et al.  Case Study: French Motor Third-Party Liability Claims , 2018 .

[50]  Robert Weidner,et al.  Classification of scale-sensitive telematic observables for riskindividual pricing , 2016 .

[51]  Y. Nesterov Gradient methods for minimizing composite objective function , 2007 .

[52]  Montserrat Guillén,et al.  Exposure as Duration and Distance in Telematics Motor Insurance Using Generalized Additive Models , 2017 .

[53]  Yoav Freund,et al.  A decision-theoretic generalization of on-line learning and an application to boosting , 1995, EuroCOLT.

[54]  J. Rosenthal,et al.  Optimal scaling of discrete approximations to Langevin diffusions , 1998 .

[55]  Eric R. Ziegel,et al.  Generalized Linear Models , 2002, Technometrics.

[56]  O. Barndorff-Nielsen Information and Exponential Families in Statistical Theory , 1980 .

[57]  Montserrat Guillén,et al.  Using GPS data to analyse the distance travelled to the first accident at fault in pay-as-you-drive insurance , 2016 .

[58]  Robert Weidner,et al.  Telematic driving profile classification in car insurance pricing , 2016, Annals of Actuarial Science.

[59]  Guangyuan Gao,et al.  Driving Risk Evaluation Based on Telematics Data , 2018 .

[60]  Simon C. K. Lee,et al.  Delta Boosting Machine with Application to General Insurance , 2018 .

[61]  Allan Pinkus,et al.  Multilayer Feedforward Networks with a Non-Polynomial Activation Function Can Approximate Any Function , 1991, Neural Networks.

[62]  Yiik Diew Wong,et al.  Developing Singapore Driving Cycle for passenger cars to estimate fuel consumption and vehicular emissions , 2014 .

[63]  N. Metropolis,et al.  Equation of State Calculations by Fast Computing Machines , 1953, Resonance.

[64]  Halbert White,et al.  Sup-norm approximation bounds for networks through probabilistic methods , 1995, IEEE Trans. Inf. Theory.

[65]  Ronald Richman,et al.  AI in Actuarial Science , 2018 .

[66]  Alois Gisler,et al.  A Course in Credibility Theory and its Applications , 2005 .

[67]  J. Rosenthal,et al.  Adaptive Gibbs samplers and related MCMC methods , 2011, 1101.5838.

[68]  Fabrizio Durante,et al.  Computational Actuarial Science with R , 2015 .

[69]  R. Tibshirani Regression Shrinkage and Selection via the Lasso , 1996 .

[70]  Guangyuan Gao,et al.  Claims frequency modeling using telematics car driving data , 2018, Scandinavian Actuarial Journal.

[71]  L. Rüschendorf,et al.  COMPLETENESS IN LOCATION FAMILIES , 2008 .

[72]  Kurt Hornik,et al.  Multilayer feedforward networks are universal approximators , 1989, Neural Networks.

[73]  Sida I. Wang,et al.  Dropout Training as Adaptive Regularization , 2013, NIPS.

[74]  Nikolaus Kriegeskorte,et al.  Robustly representing inferential uncertainty in deep neural networks through sampling , 2016, 1611.01639.

[75]  Wilfrid S. Kendall,et al.  Networks and Chaos - Statistical and Probabilistic Aspects , 1993 .

[76]  M. Kramer Nonlinear principal component analysis using autoassociative neural networks , 1991 .

[77]  Ludger Rüschendorf,et al.  An approximation result for nets in functional estimation , 2001 .

[78]  Leo Breiman,et al.  Bagging Predictors , 1996, Machine Learning.

[79]  W. K. Hastings,et al.  Monte Carlo Sampling Methods Using Markov Chains and Their Applications , 1970 .

[80]  M. Kenward,et al.  An Introduction to the Bootstrap , 2007 .

[81]  Ashutosh Kumar Singh,et al.  The Elements of Statistical Learning: Data Mining, Inference, and Prediction , 2010 .

[82]  Guangyuan Gao,et al.  Convolutional Neural Network Classification of Telematics Car Driving Data , 2018, Risks.

[83]  Kurt Hornik,et al.  Approximation capabilities of multilayer feedforward networks , 1991, Neural Networks.

[84]  Y. Makovoz Random Approximants and Neural Networks , 1996 .

[85]  J. Friedman Stochastic gradient boosting , 2002 .

[86]  H. Zou,et al.  Regularization and variable selection via the elastic net , 2005 .

[87]  Charu C. Aggarwal,et al.  Neural Networks and Deep Learning , 2018, Springer International Publishing.

[88]  J. Corcoran Modelling Extremal Events for Insurance and Finance , 2002 .

[89]  Mario Bertero,et al.  The Stability of Inverse Problems , 1980 .

[90]  R. Schapire The Strength of Weak Learnability , 1990, Machine Learning.

[91]  Razvan Pascanu,et al.  On the Number of Linear Regions of Deep Neural Networks , 2014, NIPS.

[92]  Wei-Yin Loh,et al.  Classification and regression trees , 2011, WIREs Data Mining Knowl. Discov..

[93]  Geoffrey E. Hinton,et al.  Reducing the Dimensionality of Data with Neural Networks , 2006, Science.

[94]  David Hinkley,et al.  Bootstrap Methods: Another Look at the Jackknife , 2008 .

[95]  George Cybenko,et al.  Approximation by superpositions of a sigmoidal function , 1989, Math. Control. Signals Syst..

[96]  Tom V. Mathew,et al.  Development of real-world driving cycle: Case study of Pune, India , 2009 .

[97]  Andrew R. Barron,et al.  Universal approximation bounds for superpositions of a sigmoidal function , 1993, IEEE Trans. Inf. Theory.