A novel boosting approach to actuarial ratemaking

Abstract

Successes are seen in applying advanced machine learning techniques to solve supervised learning problems in many industries. This poses a contrast to actuarial practice as most of the ratemaking exercises are still based on generalized linear modeling and averaging. This phenomenon is mainly driven by the technical challenges to adopt machine learning engines into an IT-friendly environment, non-transparent model output, and lack of regulatory acceptance. Contrarily, as the insurance industry is competitive in many markets, accurate pricing of risks is of utmost importance for insurance companies to stay relevant. This thesis offers a novel and comprehensive approach for actuaries to utilize boosting in ratemaking which addresses accuracy, transparency, robustness, and consistency. Those characteristics are crucial for actuaries to fulfill the statement of principles in ratemaking which requires a rating plan to be reasonable and not excessive, inadequate, or unfairly discriminatory.

The contributions of this thesis are three-fold. The first part of the thesis compares traditional generalized linear models to various machine learning alternatives. It confirms that a significant improvement in accuracy is observed by using machine learning techniques. This gives a strong motivation for actuaries to utilize the more complex modeling methods. A novel boosting mechanism called delta boosting, a boosting technique with actuarial focus is then introduced. Delta boosting is proven to be the optimal boosting algorithm for most common loss functions.

Poisson regression is known to underestimate the tail risk of heavy tail data commonly observed in claims data. In pursuit of finding more relevant distributions to model the claiming behavior, actuaries leverage negative binomial, zero-inflated Poisson, generalized Poisson regressions and find promising improvement. Part two of this thesis introduces a novel delta boosting implementation of negative binomial and zero-inflated Poisson. This part establishes the boosting formulae and introduces two approaches to solve for multiple parameters during the estimation process. In particular, the formula for zero-inflated Poisson regression is established to offer actuaries an intuitive view to segregate the perfect state (no propensity to claim) and non-perfect state. When compared with some popular mechanisms to handle imbalanced data, the resulting algorithm is one-shot modeling that does not require post-modeling recalibration nor judgemental distance metrics. This part of the thesis also demonstrates the flaws of common partial exposures handling and suggests that proper handling of exposures can improve the prediction accuracy.

Boosting and random forest are both members of the ensembling family of algorithms. Boosting addresses the bias reduction whereas random forest reduces the models’ variance. The third part of the thesis proposes a novel algorithm called boosting forest that combines the features of both powerful machine learning techniques and proves the merits. The random forest component allows trees with more layers to extract complex interactions in the data and averages out the noises whereas the boosting component effectively brings the model to the local minimum by reducing biases.