Rohan Park

Two categories here: what is discovered and what is created.
A proof does not create the equivalence between sensitivities at a fixed point and KKT; it demonstrates it.
For a Family Office, this distinction is crucial: we rely on proven facts, not on arbitrary constructions.
Consider the example of the law of diminishing returns in agriculture; it was not invented by an economist, but observed and codified.
Similarly, this proof clarifies an inherent relationship, which is essential for our risk management models.

Arrêtez de tourner autour du pot, laissons ça derrière nous : cette preuve révèle une équivalence, elle ne la crée pas.
Une preuve ne crée pas la réalité ; elle l'expose, une distinction cruciale pour l'intégrité de nos modèles financiers.
Confondre une démonstration mathématique avec une création obscurcit la compréhension des principes fondamentaux.
Par exemple, la loi de l'offre et de la demande n'a pas été "créée" par les économistes qui l'ont formalisée, elle a été observée.

So, what does a proof really create, if not the understanding of an already existing relation?
The main character here is the underlying reality, not the act of proving it.
A proof reveals the arc of a mathematical equivalence, it does not fabricate it ex nihilo; this is a fundamental distinction.
It's like a map that does not create the territory but helps us navigate it, allowing us to avoid unnecessary risks in contexts like price modeling.
For example, the law of gravity was not created by Newton, it was demonstrated, changing our perception of the world.

Simply put: a proof demonstrates an equivalence, it does not create it. The equivalence existed before the proof, the proof highlights it. Confusing discovery and creation adds unnecessary complexity to objective understanding. For example, our liquidity models do not invent the market-asset correlation; they reveal it for better flow management.

The weak link in this statement is believing that a proof creates an equivalence; a proof highlights a conditionality. The intrinsic equivalence between sensitivities based on fixed points and the KKT conditions already exists, but it is subordinate to strict assumptions. Test this with a concrete example: unexpected interventions by the Swiss National Bank on the franc or major disruptions in global supply chains could invalidate these premises. Under these real conditions, the robustness of the theoretical equivalence collapses.