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The topic of this lecture is stochastic calculus, which has been introduced in "Financial risk management I". We focus on the mathematical construction of this calculus. Indeed its applications to finance are developped in other lectures of the master.
Wiener Space- convergence in distribution of stochastic processes- change of time -Stochastic Differential Equations- link with Partial Differential Equations- Applications and examples (Feller non explosion tests...)
Probability- Stochastic processes (Markov Chains, Martingales).
Financial risk management I.
Some knowledge of brownian motion is required.
Final exam.
N1=E1
N2=max(N1,E2)
I. Karatzas, S.E. Shreve "Brownian motion and stochastic calculus", Springer
D. Revuz, M. Yor "Continuous martingales and brownian motion", Springer
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