图书简介
This open access book discusses the statistical modeling of insurance problems, a process which comprises data collection, data analysis and statistical model building to forecast insured events that may happen in the future. It presents the mathematical foundations behind these fundamental statistical concepts and how they can be applied in daily actuarial practice.Statistical modeling has a wide range of applications, and, depending on the application, the theoretical aspects may be weighted differently: here the main focus is on prediction rather than explanation. Starting with a presentation of state-of-the-art actuarial models, such as generalized linear models, the book then dives into modern machine learning tools such as neural networks and text recognition to improve predictive modeling with complex features. Providing practitioners with detailed guidance on how to apply machine learning methods to real-world data sets, and how to interpret the results without losing sight of the mathematical assumptions on which these methods are based, the book can serve as a modern basis for an actuarial education syllabus.
1.Introduction and discussion of statistical modeling cycle, prediction versus explanation (Breiman 2001, Shmueli 2010).- 2.Exponential dispersion family (EDF), explicit derivation based on Barndorff-Nielsen (2014) and Jorgensen (1986, 1987, 1997), discussion of the properties of the EDF.- 3.Estimation theory based on Lehmann (1959, 1983). This includes maximum likelihood estimation (MLE), uniformly minimum variance unbiased (UMVU), sufficient statistics, Cramer-Rao information bound, consistency and asymptotic normality of MLEs.- 4.Prediction theory, this includes generalization losses, deviance losses, in- and out-of-sample performance, cross-validation, Akaike’s information criterion, consistent loss functionals, proper scoring rules.- 5.Generalized linear models, this chapter is based on McCullagh-Nelder (1983) and Fahrmeir-Tutz (1994). Generalized linear models with insurance pricing application, balance property and unbiasedness, model validation, quasi-likelihoods, double generalized linear model.- 6. Bayesian methods, Markov-chain Monte Carlo (MCMC) methods, ridge and LASSO regularization, expectation-maximization (EM) algorithm, truncation and censoring. 7.- Deep learning. Feed-forward neural network, universality theorems, gradient descent algorithm and back-propagation, the balance property, bias regularization, embedding layers, auto-encoders, model-agnostic tools.- 8.Recurrent neural networks, gated-recurrent unit (GRU) networks, long short-term memory (LSTM) networks, natural language processing (NLP), word embedding.- 9.Convolutional neural networks and image recognition.- 10.Special topics such as mixture density networks (MDN), sieve estimators and asymptotic results for network predictions.
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