User:BasilNotCilantro/Nonlinear expectation/C.Hua Wang Peer Review

General info

 * Whose work are you reviewing?

C.Hua Wang


 * Link to draft you're reviewing
 * Nonlinear expectation
 * Link to the current version of the article (if it exists)
 * Nonlinear expectation

Evaluate the drafted changes
(Compose a detailed peer review here, considering each of the key aspects listed above if it is relevant. Consider the guiding questions, and check out the examples of what feedback looks like.)

From your sandbox, I found that you are trying to edit the article. It looks good. The following are my suggestions for editing.

Lead
I would suggest adding more descriptions of nonlinear expectation. Although the first sentence tries to define nonlinear expectations in this article, it is not easy to understand right now. It may be clearer if you can add some explanation sentences after the definition.

Content
1.     First of all, I think the definition also needs more explanation for people who is not good at math or statistics to understand. Second, I think the last sentence in the definition is not precise. To best of my knowledge, “monotonicity” and “constant preserving” are the constraints that the nonlinear expectations need to satisfy, while “sub-additivity” and “positive homogeneity” are the constraints for the sublinear expectations. Besides, “convexity” is another constraint for the nonlinear convex expectation. Although these expectations or constraints are somehow related, they present different meanings. Therefore, I would recommend making the definition be clearer first, and adding another section for the other constraints mentioned in the last sentence.

2.     Also, I think the example section needs more description. You can also find more examples or applications when you search the topic on the net.

Suggest resource
I would suggest you read the book “Nonlinear Expectations and Stochastic Calculus under Uncertainty.” It is free for the student at Cornell to download. Most of the information I mentioned above is in the first chapter of the book. This chapter will be really helpful for your understanding of nonlinear expectations, and the information in other chapters may help you to add more content related to this topic.

Conclusion
Overall, I think there is still a lot of room for improvement in this article. More description and explanation can help more people understand this article.

Good luck for you editing. Hope everything goes well to you. :)    C.Hua Wang