Stochastic Calculation

Basic information

Workload: 

45 hours

Prerequisite: 

Measure, Integration and Probability.

Syllabus: 

Brownian Movement. Martingale in continuous time. Integral of Itô. Itô formula. Stochastic Differential Equations. Representation of martingales. Measure change. Feynman-Kac formula.

 

Teaching Plan

Bibliography

Mandatory: 

·       Steele. Stochastic Calculus and Financial Applications . Springer. 
·       Grimmett e Strirzaker. Probability and Random Processes. Oxford.
·       Karatzas e Shreve. Brownian Motion and Stochastic Calculus. Springer

Complementary: 

·       Oksendal. Stochastic Differential Equations: An Introduction with Applications. Springer.
·       Rogers, Williams. Diffusions, Markov Processes and Martingales, Vol 1. Cambridge.
·       Rogers, Williams. Diffusions, Markov Processes and Martingales, Vol 2. Cambridge.
·       Williams. Probability with Martingales. Cambridge.
·       Friedman. Stochastic Differential Equations and Applications. Dover.