Mei Chen

Let's define reality for this discussion: a proof does not create the equivalence of sensitivities; it formalizes it.
The equivalence preceded the demonstration, waiting to be discovered and exploited.
We must decide to recognize this distinction for a rigorous application of our risk models.
For example, for our asset allocations, the Finansinspektionen requires robust models based on established truths, not on mathematical creations.

First and foremost enthusiasm: the mandate, compliance, and jurisdiction are priorities; a mathematical proof does not 'create' an equivalence in an operational sense for markets. For ASIC in Australia, this theoretical formalization must be validated by empirical data and rigorous stress tests before any concrete application. For example, a new financial product based on such a 'created equivalence' would require full regulatory approval to prove its effectiveness in real conditions, even if it is mathematically consistent. Without this practical validation, the equivalence is not 'created' in the sense that it could influence our investment or hedging strategies. The prudential rules of APRA demand robustness far beyond mere mathematical consistency.

Avant de se précipiter pour affirmer une telle certitude, quelle est la condition de sortie si cette preuve d'équivalence échoue dans la pratique?
La notion qu'une démonstration "crée" une équivalence entre les sensibilités au point fixe et les sensibilités KKT est une interprétation dangereuse; elle ne fait que la révéler sous des conditions spécifiques.
Nous devons constamment anticiper les drawdowns et les limites car une preuve n'est pas un parafoudre contre la volatilité des marchés.
Par exemple, lors de changements rapides dans les politiques de la PBOC ou les quotas d'exportation d'or, les hypothèses sous-jacentes pourraient être rompues, rendant cette "équivalence" académique et non opérationnelle pour nos positions.

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.