Stochastic Calculus

Syllabus

Brownian motion. Continous-time martingales. Itô integral. Itô formula. Stochastic Differential Equations. Martingale Representation and Backward Stochastic Differential Equations. Feynman-Kac Representation. Change of measure and Girsanov theory.

Bibliography
  • Grimmett, G. R. and Stirzaker, D. R.  (2001). Probability and Random Processes.  Oxford.

  • Steele , J. M. (2012). Stochastic Calculus and Financial Applications . Springer. 

  • Zhang, J. (2018) Backward Stochastic Differential Equations. Springer.

Exams
  • Final grade: (P1 + P2)/2

Lecture notes:
TBA de 14:20h às 16h na Sala 537 - Monitoria TBA
Homework:
  • Brownian motion

  • Itô integral and Itô formula:

  • Stochastic Differential Equations: