Hugo Chen

Let's stop going in circles; a proof does not create the equivalence it seeks to establish; it reveals it.
We must decide to be precise: the equivalence of sensitivities exists independently of its mathematical demonstration.
It's like gravity: it operated before Newton quantified it; its formula did not make it exist.
We need to set the priority on the practical application of these relationships, and not project an act of creation where there is only a discovery.
For our pension funds, this means that the fundamental principles of the market, such as price efficiency, are objective realities to manage, not malleable theoretical constructs.

Decision to make: this proof does not create the equivalence between sensitivities, it reveals it and formalizes it. The equivalence is an intrinsic property that preexisted its demonstration. Confusing proof and creation underestimates the fundamental nature of mathematical principles. For example, the proof of a geometric theorem does not make the spatial relation exist; it makes it understandable and usable. We must recognize the distinction for a rigorous predictive modeling of our actuarial hypotheses.

However, capital controls constitute a weak link, capable of breaking this equivalence in real-world situations. The substitution of the Jacobian confirms that we now need to test specifically the limits imposed by the volatility of emerging markets, where such controls are common, to determine if equation (25) holds. This is where the mechanism breaks down.

It is time to set the standard: a proof does not create an equivalence; it demonstrates it fully.
The equivalence between sensitivities at fixed points and KKT is an intrinsic property, not a fabrication.
For our actuarial commitments, we must rely on existing properties, not on a creation.
For example, the law of gravity was not created by Newton, but explained by his theory; similarly, this proof clarifies a pre-existing relationship.

Avant de s'engager, qu'est-ce qui garantit que cette équivalence des sensibilités résistera à un vrai test de marché?
Une preuve mathématique ne fait que formaliser une relation sous des conditions définies, elle ne la crée pas ex nihilo.
Si les hypothèses sous-jacentes sont violées, comme lors d'un changement imprévu de la politique de la PBOC concernant les réserves d'or, cette "équivalence" pourrait s'évaporer.
Nous avons besoin de garde-fous pour les scénarios où ces hypothèses initiales ne tiennent plus, car la protection contre les baisses est primordiale.
Par exemple, un contrôle de capitaux soudain, tel que vu en Chine, pourrait invalider les relations de sensibilité en modifiant de force les flux fondamentaux.

Who has the incentive to believe that a proof 'creates' the equivalence rather than demonstrating it? The reality is that a proof like that of the mirror descent establishes a conditional validity, it does not shape a new mathematical truth.
If everyone adopted this logic, trust in formalization would erode, somewhat like claiming that regulation of the CVM in Brazil creates market risk.
These regulations impact the payoffs and structure, but the existence of the equivalence remains independent.
An explicit proof simply establishes a preexisting relationship, making it usable under certain conditions, such as the sensitivity of gold flows to central bank decisions.