MaPhyStoCentre for Mathematical Physics and Stochastics Funded by The Danish National Research Foundation |
CAFCentre for Analytical Finance Funded by The Danish Social Science Foundation |
DYNSTOCHStatistical Methods for Dynamical Stochastic Models EU Research Training |

Aud. F, Building 534

Department of Mathematical Sciences, University of Aarhus

*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.

- 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)
- Martingales, local martingales, sigma-martingales in the continuous time case. Basic properties and theorems
- Semimartingales: basic definitions and properties. Characteristics of semimartingales, the canonical representation. Semimartingales and Lévy processes
- Sample function properties of the Lévy processes from the point of view of the semimartingale canonical representation
- Transformations of the semimartingale predictable characteristics
- Semimartingales in the mathematical finance (martingale measures and their construction, fundamental theorems of the 'Arbitrage theory')

A.S. Cherny:

- Vector stochastic integrals and stochastic integrals up to infinity
- Itô's formula and its extensions

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

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

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

- Some financial models
- Change of time for a Brownian motion
- Change of measure for Lévy processes
- 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:

- Introduction
- Basics of Lévy Processes
- Simulation and Inference for Lévy Processes
- Time Deformation and Chronometers
- Mathematics of Lévy processes
- Stochastic Volatility
- Realised Variation and Covariation
- 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/`

Martin Jacobsen (University of Copenhagen):

Jan Pedersen (University of Aarhus):

Michael Sørensen (University of Copenhagen):

Peter Tankov (Ecole Polytechnique, Palaiseau):

Jeannette H.C. Woerner (University of Oxford):

NS = Neil Shephard

FH = Freidrich Hubalek

EN = Elisa Nicolato

OBN = Ole E. Barndorff-Nielsen

AC = Alexander S. Cherny

JW = Jeannette H.C. Woerner

MJ = Martin Jacobsen

PT = Peter Tankov

JP = Jan Pedersen

HE = Hans-Juergen Engelbert

MS = Michael Sørensen

Tue. 20/8 |
Wed. 21/8 |
Thu. 22/8 |
Fri. 23/8 |
Sat. 24/8 |
Mon. 26/8 |
Tue. 27/8 |
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08.30-09.00 | Registration | |||||||

09.00-10.00 | AS | NS | AS | NS | AS | AS | AS | |

Coffee | 10.00-10.15 | |||||||

10.15-11.15 | AS | NS | AS | NS | AS | AS | NS | |

Refreshments | 11.15-11.30 | |||||||

11.30-12.30 | NS | AS | NS | AS | OBN | OBN | EN+FH | |

Lunch | 12.30-14.00 | |||||||

14.00-15.00 | NS | AS | NS | AS | EN+FH | |||

Coffee | 15.00-15.15 | |||||||

15.15-15.45 | JW | PT | JP | AC | MJ | |||

Refreshments | 15.45-16.00 | |||||||

16.00-16.30 | AC | AC | AC | AC | MS | |||

16.30-17.30 | AC | AC | AC | HE | AC |

Ole E. Barndorf-Nielsen, University of Aarhus

Bent Jesper Christensen, University of Aarhus

Albert N. Shiryaev, Steklov Institute, Moscow

Michael Sørensen, University of Copenhagen

Do not hesitate to contact the MaPhySto secretariat
(at `maphysto@maphysto.dk`

) for more information.

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

This document, *http://www.maphysto.dk/oldpages/events/LPS2002/index.html*,
was last modified
January 19, 2004.
Questions or comments to the contents of this document should
be directed to `maphysto@maphysto.dk`.