Stochastic Calculus: An Introduction with Applications

A course book that goes from option pricing basics to martingales, Brownian motion, Wiener and Itô integrals and Itô's formula. It ends by deriving and solving the Black-Scholes partial differential equation.

Michael J. Kozdron

Graduate lecture notes on continuous-time finance: options and arbitrage, the Black-Scholes model, stochastic integration and pricing in complete markets. A solid bridge between probability theory and financial models.

Universität Münster

Lecture notes on Brownian motion, local martingales, Itô integration, Itô's formula and stochastic differential equations. Rigorous and compact, with pointers to the standard references.

David Prömel, Mathias Trabs

Covers the core of stochastic analysis, including Itô's formula, martingale representation and Girsanov's theorem, then moves to stochastic differential equations and the Feynman-Kac formula. The final part applies these tools to quantitative finance.

Melih İşeri