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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
Homework:

  • Brownian motion

  • Itô integral

  • Itô formula

  • Stochastic Differential Equations

  • Feynman-Kac

  • Martingale Repr. and Girsanov 

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