Finite-sample valid prediction of future insurance claims in the regression problem

Prediction is one of the most important inferential tasks for actuaries since it forms the basis for many key aspects of an insurer's business operations, such as premium calculation and reserves estimation. According to Shmueli (2010), there are two key goals in data science and statistics: to explain and to predict. However, these two goals often warrant different approaches. For example, as demonstrated in Shmueli (2010), a wrong model, under some conditions, can even beat the oracle model in prediction, but the same cannot be said for explanation. This paper only concerns prediction. In the existing insurance literature, prediction is often performed using either a parametric approach or a non-parametric approach (e.g., Frees et al. 2014). In the parametric approach, the actuary posits a model, applies model selection tools to choose the "best" model, trains the chosen model, and finally makes predictions; see, for example, Claeskens and Hjort (2008) and Part I of Frees (2010). While this parametric approach has been widely applied in insurance, it has several drawbacks. First, the posited model may be misspecified, leading to grossly misleading predictions (Hong and Martin 2020).