Martingales

Risk-Neutral Probabilities Explained ArXiv ID: ssrn-1395390 “View on arXiv” Authors: Unknown Abstract All too often, the concept of risk-neutral probabilities in mathematical finance is poorly explained, and misleading statements are made. The aim of this paper Keywords: risk-neutral probabilities, martingales, stochastic calculus, derivatives pricing, Quantitative Finance Complexity vs Empirical Score Math Complexity: 7.0/10 Empirical Rigor: 2.0/10 Quadrant: Lab Rats Why: The paper focuses on theoretical foundations, including continuous-time stochastic processes like geometric Brownian motion and martingales, but lacks any empirical backtesting, data, or implementation details. flowchart TD A["Research Goal: Explain Risk-Neutral Probabilities clearly"] --> B["Methodology: Critical Review of Stochastic Calculus"] B --> C["Input: Misleading Statements in Texts"] C --> D["Computational Process: Martingale Measure Derivation"] B --> E["Input: Derivatives Pricing Models"] E --> D D --> F["Key Finding: Q-Measure vs. P-Measure"] D --> G["Key Finding: No-Arbitrage Pricing Framework"]

MathematicalFinanceIntroduction to Continuous Time Financial Market Models ArXiv ID: ssrn-976593 “View on arXiv” Authors: Unknown Abstract These are my Lecture Notes for a course in Continuous Time Finance which I taught in the Summer term 2003 at the University of Kaiserslautern. I am aware that t Keywords: continuous time finance, stochastic calculus, option pricing, martingales, stochastic differential equations, Derivatives / Quantitative Finance Complexity vs Empirical Score Math Complexity: 8.5/10 Empirical Rigor: 1.0/10 Quadrant: Lab Rats Why: The paper presents dense, advanced mathematics centered on stochastic analysis, stochastic calculus, and derivations of the Black-Scholes model, with no empirical data or backtesting. flowchart TD A["Research Goal: Develop Continuous Time Financial Market Models"] --> B["Methodology: Stochastic Calculus & Martingales"] B --> C["Data: Geometric Brownian Motion SDE Inputs"] C --> D["Computation: Black-Scholes Option Pricing & PDE Solution"] D --> E["Outcome: Valuation of Derivatives & Risk Management Insights"]