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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
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Steele , J. M. (2012). Stochastic Calculus and Financial Applications . Springer.
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Grimmett, G. R. and Stirzaker, D. R. (2001). Probability and Random Processes. Oxford.
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Zhang, J. (2018) Backward Stochastic Differential Equations. Springer.
Exams and Anouncements
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P1 (matéria: esperança condicional, martingais, movimento Bronwiano, integral de Itô)
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P2 (matéria: fórmula de Itô, EDE, representação martingal, Feynman-Kac, Girsanov)
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Nota final: 0.3 * P1 + 0.3 * P2 + 0.4 * (média das listas)
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