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Stochastic Calculus

Syllabus

Conditional Expectation. Discrete-time martingales. Brownian motion. Continuous-time martingales. Itô integral. Itô formula. Stochastic Differential Equations. Martingale Representation. Feynman-Kac Representation. Change of measure and Girsanov theory.

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

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

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

Exams and Anouncements
  • P1 (matéria: esperança condicional, martingais, movimento Bronwiano, integral de Itô)

  • P2 (matéria: fórmula de Itô, EDE, representação martingal, Feynman-Kac, Girsanov)

  • Nota final: 0.3 * P1 + 0.3 * P2 + 0.4 * (média das listas)

Lecture notes:
Homework:
  • Probability (Review)  

  • Cond. Expectation          Entrega: 13/1

  • Martingales                     Entrega: 22/1 (primeira) e 27/1 (segunda)

  • Brownian motion           Entrega: 22/1

  • Itô integral           Entrega: 27/1

  • Itô formula           Entrega: 3/2

  • Stochastic Differential Equations          Entrega: 10/2

  • Feynman-Kac          Entrega: 19/2

  • Martingale Repr. and Girsanov          Entrega: 19/2