Mathematical Principles and Quantitative Finance · 01. octobre 2024
En mathématiques, la continuité est un concept fondamental qui nous aide à comprendre le comportement des fonctions. Si la notion standard de continuité est généralement suffisante pour les applications de base, il existe une version plus forte, appelée continuité uniforme. Heinrich Heine a introduit le concept de continuité uniforme en 1872 lorsqu’il a publié une démonstration du théorème aujourd’hui connu sous le nom de théorème de Heine pour les fonctions continues sur un...
Mathematical Principles and Quantitative Finance · 01. octobre 2024
Uniform continuity is a key concept in mathematical analysis that extends the standard idea of continuity by ensuring consistent behavior of functions across entire intervals. Introduced by Heinrich Heine in 1872 and rooted in earlier work by Dirichlet (1854), it plays a critical role in advanced mathematics and real-world applications.
Pointwise Continuity: Focuses on local behavior at individual points.
Uniform Continuity: Ensures predictability across an entire domain using
Stochastic Models and Processes · 03. novembre 2023
The Cheyette Model is a complex financial tool for predicting interest rate movements, accounting for time-varying mean reversion and volatility. It's more intricate than simpler models like Vasicek due to its detailed parameters, which makes it robust but computationally intensive and less commonly used in practice.