Stochastic Differential Equations

Macroscopic Market Making ArXiv ID: 2307.14129 “View on arXiv” Authors: Unknown Abstract We propose a macroscopic market making model à la Avellaneda-Stoikov, using continuous processes for orders instead of discrete point processes. The model intends to bridge the gap between market making and optimal execution problems, while shedding light on the influence of order flows on the optimal strategies. We demonstrate our model through three problems. The study provides a comprehensive analysis from Markovian to non-Markovian noises and from linear to non-linear intensity functions, encompassing both bounded and unbounded coefficients. Mathematically, the contribution lies in the existence and uniqueness of the optimal control, guaranteed by the well-posedness of the strong solution to the Hamilton-Jacobi-Bellman equation and the (non-)Lipschitz forward-backward stochastic differential equation. Finally, the model’s applications to price impact and optimal execution are discussed. ...

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"]