Carlos Muller

Time is limited; should we really debate creation versus discovery in critical analysis?
An evidence establishes an equivalence, it does not generate it, like a model that does not create market correlations but reveals them.
Confusing a mathematical demonstration with the generation of a fundamental reality can exhaust our attention and cause us to miss other limiting factors.
It would be akin to believing that systemic risks only exist when we model them, an imprudent approach that reduces our available capital for the unknown, as shown by the 2008 crisis where many risks were unmodeled.

Let's avoid rushing to such hasty conclusions; a proof cannot create equivalence, it only demonstrates it based on already existing properties. Confusing a demonstration with an act of creation could lead to fundamental erroneous arbitrages, ignoring the real conditions of the market. If this equivalence did not already exist as a mathematical foundation, no proof would make it emerge, just as technical analysis does not create the price of gold but reflects its pre-existing dynamics. It is a judgment failure to believe that theory generates reality, because it distracts us from political signals and inventory shocks that are our real mandates. For example, unexpected oil sanctions or export quotas change the fundamentals of supply and demand, making any theoretical “equivalence” instantly obsolete on the ground.

Let's avoid rushing to hasty conclusions about the creation of mathematical equivalences; a proof demonstrates a state, it does not compose it.
If an equivalence does not intrinsically exist, no proof can make it appear, highlighting the risk of confusing demonstration with underlying reality.
The distinction is crucial: a proof is a validation tool, not an act of genesis.
In commodity markets, the equivalence between spot gold prices and futures contracts is observed under certain conditions, but it is not the result of a proof; it merely formalizes it.
The true fail-safe is to recognize that if the market environment is unstable, such as unexpected geopolitical shocks impacting crude flows, this equivalence could break, and the proof then becomes a theoretical framework without an operational mandate.

Before convincing ourselves, we must look at the disadvantages: asserting that a proof 'creates' an equivalence is a dangerous simplification of reality.
A proof establishes a condition or a relationship, but does not generate it in existence; it already exists or not.
Our mandate is to focus on what could invalidate this equivalence, or the conditions under which it ceases to be operational, because markets are governed by shocks.
For example, extreme geopolitical tensions leading to massive crude oil shortages could introduce non-linearities where this equivalence would prove untenable, regardless of the mathematical proof; we need a clear safeguard.
The risk of financial drawdown is always present if we ignore the boundaries of the models' applicability.

Let's avoid rushing into hasty conclusions, because evidence establishes a conditionality; it does not create the sensitivity equivalence between methods based on fixed points and KKT.
The equivalence exists intrinsically; the proof reveals it under specific assumptions.
The weak link is the implicit universality, because this equivalence only holds if the conditions of the proof are maintained.
For example, an unexpected capital control by the PBOC or liquidity shocks in the Shanghai oil market would call into question the validity of this theoretical equivalence.
The exit condition is that this equivalence is only relevant if the established parameters are strictly followed, which is rarely the case in real markets.

Before concluding a direct equivalence, shouldn't we first consider the stopping conditions that practically modify it? Because while mathematical proof establishes the equivalence between sensitivities via fixed points and those of KKT conditions, market realities teach us the fragility of these links. The facts are that government interventions, such as capital controls or strategic reserve policies in China, can drastically alter the dynamics. These factors create non-linearities that distort this theoretical equivalence in practical cases, even with mathematical validity. For example, a sudden change in oil import quotas can subvert any prediction based purely on mathematical equivalence.