VaR Monotone work -- NOT ready to be merged! #42
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My idea is to define VaR and quantile by their properties rather than by how they would be computed, I will try to add some of these ideas to the branch. |
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Caleb also had some ideas and came up with a new definition for VaR that converts the finite set of rational numbers to a finite set of integers, which does have a minimum (shift it up to be a finite set of natural numbers, take the minimum, and then shift it down). |
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Here are Caleb's notes. He did Q+ -> Natural numbers here but with a little work we can change it to just Q -> integers
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Here is my current work towards proving the monotonicity of VaR is here. I did redefine VaR over the reals, but I am now thinking I should just try to make it work in Q because I'd need to redefine too many definitions in terms of R, which is not the direction we want to go. I did prove the monotonicity of cdf.