programma prof Di Nunno

Introduction to stochastic calculus and stochastic differential equations

Abstract.
In this intensive course of 8 lectures, we will introduce the audience to Ito non anticipating calculus and stochastic differential equations. In specific, the topics treated will include:
- Construction of the Ito integral
- Possible extensions to the construction
- Properties of the process of the Ito integrals: martingales
- Integral representation theorems  and martingale representation theorems
- Stochastic differential equations (SDEs): existence and uniqueness of a strong solution
- Solution to some SDEs and general solution to linear SDEs
- The Girsanov theorem and SDEs under change of measure

Possible seminar topics:
- The Ito integral and the self-financing condition in finance
- Integral representation theorem and backward stochastic differential equations
- The Girsanov theorem and its application to finance
- Elements of filtering
- Komogorov backward equation - application to Black and Scholes formula
- Random time changes
- Beyond Brownian motion

Books:

Main reference:
Bernt Øksendal
Stochastic Differential equations
(An introduction with applications)
6th edition
Springer

About the lecturer: http://folk.uio.no/giulian/



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Giulia Di Nunno
Professor
Centre of Mathematics for Application
Department of Mathematics
University of Oslo