Insurance Pricing with Deep Bayesian Neural Networks

With the emergence of data analytics and artificial intelligence in the insurance industry, non-life insurance actuaries have many flexible tools to improve the predictive performance of their pricing and reserving models. However, a major inconvenience with the popular algorithms for machine learning regression (gradient boosting machines and neural networks) is that they predict point estimates instead of probability distributions and ignore the uncertainty of the model parameters. In addition, these models cannot easily accommodate multivariate dependent random variables as outputs. These shortcomings may substantially impact the uncertainty of pricing and reserving models for a non-life insurer since one requires more than point estimates for quantitative risk management. Therefore, actuaries, risk managers and insurance regulators should be aware of these issues and, ideally, measure and account for the understated uncertainty of predictions. In this talk, we present a multivariate deep Bayesian neural network for insurance pricing, a flexible machine learning framework that captures process and parameter uncertainties. The multivariate deep Bayesian neural network is a flexible model that may approximate any multivariate distribution function. We construct this model through three components.

1. A neural network model with a likelihood loss function to capture process uncertainty.
2. A Bayesian construction to capture parameter uncertainty.
3. A Bernstein copula to capture the dependence between the components of the multivariate model.

By studying neural networks within the Bayesian framework, we capture both process and parameter uncertainty of predictive models, providing better tools to diagnose whether the model predictions are confident or not. Further, knowledge of the uncertainty associated with the model parameters enables actuaries to make an adequate tradeoff between the flexibility and the stability of premium predictions, reducing overfitting. This talk introduces the model, proposes methods to estimate the parameters and compares estimation strategies based on variational inference. Finally, we provide practical insights on model construction and calibration with a case study.

Find the Q&A here: Q&A on 'Insurance Pricing and Maching Learning'