A vast and growing literature on explaining deep learning models has emerged. This paper contributes to that literature by introducing a global gradient-based model-agnostic method, which we call Marginal Attribution by Conditioning on Quantiles (MACQ). Our approach is based on analyzing the marginal attribution of predictions (outputs) to individual features (inputs). Specifically, we consider variable importance by fixing (global) output levels, and explaining how features marginally contribute to these fixed global output levels. MACQ can be seen as a marginal attribution counterpart to approaches such as accumulated local effects, which study the sensitivities of outputs by perturbing inputs. Furthermore, MACQ allows us to separate marginal attribution of individual features from interaction effects and to visualize the 3-way relationship between marginal attribution, output level, and feature value.

We study the optimal insurance design problem. This is a risk sharing problem between an insured and an insurer. The main novelty in this paper is that we study this optimization problem under a risk-adjusted premium calculation principle for the insurance cover. This risk-adjusted premium calculation principle uses the cost-of-capital approach as it is suggested (and used) by the regulator and the insurance industry.

The Munich chain-ladder method for claims reserving was introduced by Quarg and Mack on an axiomatic basis. We analyze these axioms, and we define a modified Munich chain-ladder method which is based on an explicit stochastic model. This stochastic model then allows us to consider claims prediction and prediction uncertainty for the Munich chain-ladder method in a consistent way.