Imagine a play where the playwright writes a happy ending – does it create happiness in the real world, or does it describe it under certain conditions?
A mathematical proof demonstrates a link, but it does not make it exist absolutely, especially for the equivalence of sensitivities between fixed points and KKT.
The course of this proof sometimes neglects the risks of the market.
Market actors, like a regulator changing rules for French banks facing a liquidity crisis, can alter these fundamental conditions.
The validity of this equivalence would then be compromised by these external shocks, making the proof more of a compass rather than an immutable map.