Rohan Rossi

There are two categories of relationships here: those that are discovered and those that are created.
A proof, such as that of the equivalence between sensitivities by fixed point and KKT sensitivities, falls into the first category; it reveals an existing truth, rather than inventing it.
For an Australian Family Office, this is crucial, because our investment decisions rely on verifiable and intrinsic market relationships, not on ephemeral hypotheses.
The pre-existing mathematical equivalence was there, and the proof merely formalizes it for practical application, for example by enabling better quantitative modeling of risk factors.
It's like the effect of a rate hike on real estate prices: the relationship existed before economists proved and modeled it.

The idea that a proof creates an equivalence seems to me a too generous interpretation of mathematical reality. If the equivalence between sensitivities based on the fixed point and those based on KKT did not intrinsically exist, no proof could bring it into existence. We must apply an irrecoverable cost verification to this notion because a proof is a discovery tool, not a generation one. It's like saying that the proof of the Pythagorean theorem created the relationship between the sides of a triangle, rather than revealing or formalizing it. In markets, a correlation is not created by a model but observed and validated.

Let's define the level. A proof does not create the equivalence; it reveals it. The equivalence exists independently of its demonstration. Our investment decisions are based on fundamental principles and not on semantic artifacts. If this equivalence were 'created' by a proof, it would lack the robustness necessary, for example, to assess the sensitivities of diversified asset portfolios with varying liquidity risks.

Isn't it more accurate to consider that a mathematical proof demonstrates an equivalence rather than creates it? Asserting that a proof 'creates' an equivalence risks leading to an ontological confusion and could mislead about the nature of our models. While formalization is crucial for our understanding, it does not generate the existence of an underlying relationship. Financial principles, such as the balance of interest rates or hedging strategies, preexist their modeling. For example, the equivalence between covered and uncovered interest rate parity exists independently of its formal proof; it describes a market behavior.

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.