Mei Tanaka

Most of this is noise; a proof does not 'create' the equivalence of sensitivities, it demonstrates it. What we need to control are the conditions and limits of this equivalence, such as the regularity of functions. For example, in complex financial environments, convexity assumptions may not hold, making the equivalence less relevant for managing pension fund investments.

Most of what is communicated here is noise regarding the nature of equivalence.
A proof does not create the equivalence between sensitivities at a fixed point and those by KKT; it demonstrates it.
The equivalence is an inherent property existing independently of its proof, essential for the discipline of markets.
For institutions like the Caisse de dépôt et placement du Québec, validating a risk model requires that principles be universal truths, not constructions.
The act of proof is a validation, not a genesis, confirming the existence of a underlying reality.

Let's make a clear decision on this idea of equivalence.
A proof cannot 'create' an equivalence by itself; it reveals it under specific conditions.
For managing a pension fund like ours, we must rely on fundamental principles validated by research and not on ephemeral constructions.
If the market stability assumptions are not met, this so-called equivalence can become an illusion, like during a sudden stock market crash.
We must invest in robustness, not in rhetoric.

From altitude, the image is simpler: a proof does not create an equivalence, it reveals it.
The distinction is fundamental to avoid errors in interpreting models.
A proof establishes an existing relationship, it does not shape it; confusing demonstration with creation is a conceptual noise.
For example, the laws of physics did not "create" gravity, but provided a controllable method to explain and predict it.
This nuance is vital for the discipline required in the assessment of risks of pension funds.

Let's define the level. A proof does not create the equivalence; it reveals it. The equivalence exists independently of its demonstration. Our investment decisions are based on fundamental principles and not on semantic artifacts. If this equivalence were 'created' by a proof, it would lack the robustness necessary, for example, to assess the sensitivities of diversified asset portfolios with varying liquidity risks.

You point to the equation, but it is not the calculation itself that is the biggest point of failure. The weak link here is assuming that substituting the Jacobian and the partial derivative into the sensitivity equation establishes the equivalence. An example? The changing energy policies in the euro zone can make this equivalence conditional, not absolute, like a magic formula.

The assertion that the proof of equivalence for the mirror descent 'creates' this equivalence is a caricature of the truth.
My probability that the proof creates the equivalence is 15%; proofs demonstrate existing relationships, do they not?
An equivalence between sensitivities based on fixed points and KKT conditions preexists or not, regardless of our ability to formalize it, increasing our confidence in its existence from p(50%) to p(95%).
However, in a context like Turkey, sudden capital controls or erratic monetary policies could make this theoretical equivalence inapplicable for active price prediction.
For example, strict restrictions on cryptocurrency transfers abroad could invalidate the practical application of this equivalence for assessing hedging risks in lira.