MaPhySto Centre for Mathematical Physics and Stochastics Funded by The Danish National Research Foundation	CAF Centre for Analytical Finance Funded by The Danish Social Science Foundation	DYNSTOCH Statistical Methods for Dynamical Stochastic Models EU Research Training

Summer School organized jointly by CAF, DYNSTOCH and MaPhySto

From Lévy Processes to Semimartingales - Recent Theoretical Developments and Applications to Finance

Content:

• Introduction to Semimartingales and their Basic Algebra. Lectures by Albert N. Shiryaev, Steklov Institute, Moscow
• Change of Time and Measure. Lectures by Albert N. Shiryaev, Steklov Institute, Moscow
• Stochastic Volatility Models and some of their Applications. Lectures by Neil Shephard, Nuffield College, Oxford, Ole E. Barndorff-Nielsen, MaPhySto, Aarhus, Friedrich Hubalek, Vienna University of Technology, and Elisa Nicolato, Department of Mathematical Sciences, University of Aarhus.

In addition to the lecture series there will be several invited talks, and some tutorial classes.

Contents of Lecture Series:

1. Martingale approach to the study of stochastic processes with discrete time (martingales, local martingales, Doob's decomposition, stochastic exponential and stochastic logarithms, jump measures, compensators)
2. Martingales, local martingales, sigma-martingales in the continuous time case. Basic properties and theorems
3. Semimartingales: basic definitions and properties. Characteristics of semimartingales, the canonical representation. Semimartingales and Lévy processes
4. Sample function properties of the Lévy processes from the point of view of the semimartingale canonical representation
5. Transformations of the semimartingale predictable characteristics
6. Semimartingales in the mathematical finance (martingale measures and their construction, fundamental theorems of the 'Arbitrage theory')

A.S. Cherny:

1. Vector stochastic integrals and stochastic integrals up to infinity
2. Itô's formula and its extensions

Change of Time and Measure (A.N. Shiryaev):

1. Change of time (basic definitions, constructions, properties)
2. Time-change representations of stochastic processes (in the strong and the weak sense)
3. Change of time in the stochastic integrals
4. Change of measure (absolute continuity and singularity, Lebesgue decomposition, Girsanov type theorems)
5. Fourier and Laplace cumulant processes. The Esscher change of measure
6. Change of measure and pricing and hedging

Change of Time and Measure for Lévy Processes (A.S. Cherny):

1. Some financial models
2. Change of time for a Brownian motion
3. Change of measure for Lévy processes
4. Change of time for Lévy processes

Stochastic Volatility Models and some of their Applications (N. Shephard and O.E. Barndorff-Nielsen):

The lectures will partly be based on draft material for a book with the working title Lévy Processes, Stochastic Volatility, Power Variation and Financial Econometrics. The chapter headings for the book are:

1. Introduction
2. Basics of Lévy Processes
3. Simulation and Inference for Lévy Processes
4. Time Deformation and Chronometers
5. Mathematics of Lévy processes
6. Stochastic Volatility
7. Realised Variation and Covariation
8. Power Variation

Additional topics will be pricing of derivatives under stochastic volatility models and multivariate extensions. Much of the research work to be discussed is also available in a series of recent paper that may be accessed at the web address http://www.levyprocess.org/

Additional Lectures:

Time Schedule:

Social Events:

Support:

Organizers:

Ole E. Barndorf-Nielsen, University of Aarhus
Bent Jesper Christensen, University of Aarhus
Albert N. Shiryaev, Steklov Institute, Moscow
Michael Sørensen, University of Copenhagen

List of Participants

Here you can download the papers from the lectures given by Alexander Cherny and Albert Shiryaev

More Information:

Do not hesitate to contact the MaPhySto secretariat (at maphysto@maphysto.dk) for more information.

(This announcement in [ postscript-format | pdf-format ])