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@voceesabio: 🧠 Você sabia que repetir uma informação muitas vezes pode fazer ela parecer mais verdadeira? Esse efeito psicológico é conhecido como efeito da verdade ilusória.

você é sábio
você é sábio
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Region: BR
Monday 07 September 2026 01:07:00 GMT
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guitux1
Guitux :
já entendi tudo
2026-09-08 01:41:00
0
alexandrafleitee
Alexandra Figueiredo :
exatamente
2026-09-07 11:00:36
0
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Why I believe math is an art. This is a clip taken from a longer vlog I haven’t posted yet, where im trying to explain why I think math/physics is an artistic endeavor. I bring up an example of how you can derive the SABR model (a model in quantitative finance used for interest rates) with differential geometry instead of the usual perturbation theory way. This is genuinely one of the coolest things I’ve taught myself and wanted to share. (For the nerds) I posted my full 18 page derivation on June 18 2025 (different post you can check out if u want!). The main idea was to get the SABR PDE, transform it into the Eikonal (Hamilton-Jacobi) equation via a WKB/Laplace ansatz, and then reinterpret it as a 2D Riemannian manifold (with one dimension being the forward process, and the other the stochastic volatility process). Then use differential geometry for the most part to solve the rest. I thought it was really elegant how you can combine something like a WKB ansatz (which has its roots in quantum mechanics) with Riemannian geometry techniques (popular in general relativity). This was the logic of the derivation: SABR SDE ➡️Feynman-Kac (via multivariate Itô lemma) ➡️Backward pricing PDE ➡️WKB/Laplace ansatz ➡️Matched asymptotic expansion (identify leading order tau^(-2) terms) ➡️Eikonal (Hamilton-Jacobi) equation ➡️2D Riemannian manifold structure ➡️Covariant metric tensor ➡️Geodesic distance functional ➡️Christoffel symbols ➡️Riemann curvature tensor ➡️Ricci tensor ➡️Ricci scalar ➡️Laplace-Beltrami operator ➡️Curved space heat kernel (Gaussian + Van Vleck determinant & Ricci correction) ➡️Integration against European call payoff (Gaussian integrals A0-A4) ➡️ Near-ATM volatility smile ➡️Final SABR formula #quant
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