Advanced Financial Mathematics: Lecture Notes

A clear introduction to stochastic calculus by a leading probabilist, from discrete martingales and Brownian motion to Itô's formula and stochastic differential equations. Examples from finance appear throughout, with exercises in every chapter.

Gregory F. Lawler

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

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