12. septembre 2023

Riemann & Lebesgue! Riemann uses x-axis vertical slices; Lebesgue opts for y-axis horizontals. Jumpy functions? Lebesgue handles with grace. In finance's unpredictable leaps, this is invaluable. Where traditional methods waver, Lebesgue stands firm, mirroring market's capricious beats. Experience the mathematical elegance in navigating financial unpredictability! #RiemannVsLebesgue #QuantitativeFinance 📈📊🔢📉

II. Mathematical Tools and Principles · 03. juin 2023

In finance, Jensen's inequality showcases convexity's power. For a function to be convex, its second derivative is positive, affecting bond prices & options pricing. The inequality states that for convex functions, the expected value of the function exceeds the function of the expected value. In option strategies, even if the average expected price matches the strike, convexity ensures a positive expected payof

15. avril 2023

Brownian motion describes random particle movement in a fluid, often used to model stock prices. Geometric Brownian motion, an extension, incorporates trends in stock prices, making it suitable for financial markets. While both capture randomness, geometric Brownian considers consistent growth or decline over time, offering a more nuanced perspective for investors. #BrownianMotion #GeometricBrownianMotion #FinancialModeling #StockMarketAnalysis #InvestmentTools

I. Stochastic Models and Processes · 08. avril 2023

Imagine the stock market as a rollercoaster, with predictable ups and downs but also unexpected twists. The stochastic differential equation (SDE) is like a map predicting this ride. It considers both the general trends and sudden shifts, helping investors foresee potential stock moves. Just as weather forecasts predict sunshine or rain, the SDE estimates stock price changes. Dive into the math behind market predictions! #StockMarket #SDE #InvestingBasics #FinancialForecasting #MarketTrends