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Advanced Stochastic calculus

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  • Number of hours

    • Lectures : 18.0
    ECTS : 1.75

Goals

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.


Contact Pierre ETORE

Content

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...)



Prerequisites

Probability- Stochastic processes (Markov Chains, Martingales).

Financial risk management I.

Some knowledge of brownian motion is required.

Tests

Final exam.



N1=(2*E1+CC)/3
N2=max(N1,0.5*(N1+E2))

Additional Information

Curriculum->For Financial Engineering->Semester 5

Bibliography

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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Université Grenoble Alpes