Machine Learning in Insurance industry
I haven't seen the specifical cases you mention , but I know of machine learning within insurance, and the types of models I've seen being used always depended on the criticality of the data and use of the results.

So a more general answer: if they need to justify all modelling decisions (as is often the case in insurance), they stick to more traditional models, such as logistic regression, tree-based methods and the like. More cutting-edge models are considered black-boxes.

If the project if more about analysing ad-hoc topics and non-core businesses, but which could perhaps support core business decisions (or otherwise), then anything is game: from stacked bidirectional LSTMs on word embeddings of their contracts to capsule networks on images scraped from social media websites.

I suppose you could model Moral Hazard similarly to fraud, in which case there are plenty of examples to be found online. I think there was even a Kaggle competition on that.