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
In the study of mathematical analysis, continuity is a cornerstone concept that helps us understand the behavior of functions. While the standard notion of continuity is often sufficient for basic applications, there exists a stronger version known as uniform continuity. Heinrich Heine introduced the concept of uniform continuity in 1872 when he published a proof of the theorem now known as Heine's theorem for continuous functions on a segment. However, the idea and proof originally came from...
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.