Stochastic Calculus, Filtering, and Stochastic Control

Author: Ramon van Handel
Type: Study Notes, Lecture Notes, e-book
Level: MSc(Math. Fin), Ph.D.(Fin)

These lecture notes for the course "Stochastic Calculus and Stochastic Control" from Ramon van Handel are an excellent coverage of the topic. The notes are very intuitive and thus are appropriate for readers with major other than mathematics. The lecture notes provide the necessary background, probability theory, stochastic processes, martingales, the wiener process (Brownian motion). Stochastic integrals, Itō's lemma and stochastic differential equatios (SDEs) are covered in later chapters. After the necessary background, optimal control and filtering theory are covered next. Optimal stopping is discussed in the final chapter.

You can download Ramon van Handel's "Stochastic Calculus, Filtering, and Stochastic Control" using the following link

Stochastic Calculus

Author: Alan Bain
Type: Study Notes, Lecture Notes
Type: Advanced Undregraduate(Math), MSc(Math. Fin), Ph.D.(Fin)

These notes provide an introduction to the basics of stochastic integration with respect to continuous semimartingales. They contain all the theory usually needed for basic mathematical finance such as Girsanov theorem (change of measure). The topic of stochastic differential equations (SDEs) is also covered as well as the relations with partial differential equations (Feynman-Kac Representation).

You can download Alan Bain's "Stochastic Calculus" using the link that follows