Anna Dubois

The concept of 'creation' is a luxury we cannot afford; attention is a finite resource and is becoming scarce.
A proof reveals a preexisting mathematical truth, it does not generate it as if it were an innovation.
Focusing on the semantics of 'creation' distracts from the essential: the robustness and practical applicability of the equivalence.
For critical investment decisions, we must rely on equivalences that hold under real market conditions, not on academic distinctions.
For example, an equivalence demonstrated for perfect markets could prove unnecessarily fragile in the volatile context of emerging markets in sub-Saharan Africa and cause us to miss opportunities.

Simple substitution in an equation does not create equivalence. Before proceeding, one must consider that this equivalence is more of a condition than a direct consequence, and it heavily depends on the stability of the underlying assumptions. For example, even a minor break in the convexity of the problem could invalidate such an assumption of equivalence.

Before convincing oneself, one must consider the downside. The idea that evidence reveals a conditionality, rather than creating an equivalence, is an essential warning. If this intrinsic equivalence is dependent on strict assumptions, which makes it vulnerable, the integration of volatile market conditions or unforeseen exogenous shocks, such as a major global pandemic, into sensitivity models is an essential step of caution. This allows determining whether the equilibrium persists in extreme situations, which is the mandate of this type of analysis.

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.

The establishment of this equivalence through the substitution of the Jacobian and the partial derivative in the sensitivity equation is certainly a step. However, it highlights the need to validate these calculations through market scenarios where real frictions, such as bottlenecks in the labor market, can introduce significant divergences. Additional work on the liquidity data of emerging markets is therefore a prerequisite.

Before there is a conviction, one must understand the risk: the idea that proof creates the equivalence is difficult to accept. A proof does not bring the implicit market relation into existence; it formalizes it and delineates the threshold of application. If this equivalence depended on proof for its existence, what would protect us in case of failure of the proof or changing conditions? For example, the relation between the PBoC's gold volumes and liquidity exists, whether we have an elegant proof or not; proof only confirms it. We must remain vigilant about conditions that could render the proof ineffective, such as unexpected changes in Chinese regulation on futures markets.