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SECOND ANNOUNCEMENT
SUMMER SCHOOL ON STOCHASTICS AND FINANCE
Mathematical Finance is a field that has been rapidly
growing in different directions. The purpose of this advanced course is
to provide a forum to people interested in the recent developments of the
theory.
The main focuses of the course will be on hedging and
modelling. This advanced course will have two main series of 5 one hour
and a half lectures. The first course will be on
"Recent Developments in Hedging", by
Prof. I Prof. Ioannis Karatzas,
Eugene Higgins Professor of Applied Probability
Department of Mathematics
Department of Statistics
Columbia University
http://www.stat.columbia.edu/~ik/
1) Introductory Lecture: Models, Basic Problems,
Black-Scholes
2) Hedging under Constraints: European Contingent
Claims
3) Hedging under Constraints: American Contingent
Claims
4) Problems of Partial Hedging and Hypothesis Testing
5) Least-Squares Approximation of Random Variables
by Stochastic Integrals;
The second course will be on
"Change of time and change of measures with applications
to the modelling in financial economics" by
Prof. Albert N. Shiryaev
Steklov Mathematical Institute
Moscow,
http://www.ras.ru/local.docs/mian/statstoch.html
The contents of the course will be
1-2) Time change: basic definitions, constructions,
properties, change-time representations of the processes X in strong (X=YoT,
a.s) and weak (X=YoT, in law) senses, via "simple" processes Y (Brownian
motion, Lévy processes,...) and a change of time T.
2-3) Time change and integral representations:
strong representations of the local martingales and weak representations
(X=H·B+W*(p-q) with a Brownian motion and a Poisson measure).
3-4) Integral transformations Xf =
f·X of semimartingales and change of measures: cumulant function
Kf and a triplet (Bf, Cf, vf)
of the processes Xf; Girsanov's theorems, Esscher's type change
of measures.
4-5) Applicattions to the modelling in
the financial economics: conditions of the absence of arbitrage, stochastic
volatility models; innovation, devolatilization, filtering, statistical
problems in the analysis of the financial data.
There will also be two other smaller short courses as follows:
Lévy systems in Finance
Levy based dynamic models for financial economics.
Prof. Dilip Madan
University of Maryland at College Park
College of Business and Management,
http://alexandra.bmgt.umd.edu/~dmadan/
Slides: 1, 2,
3
Asset Prices are Brownian motion: only in Business Time
Purely Discontinuous Asset Price Processes
Stochastic Volatility for Lévy Processes
Option Valuation Using the Fast Fourier Transform
Optimal Investment in Derivative Securities
The Variance Gamma Process and Option Pricing
Prof. Ole E. Barndorff-Nielsen
Aarhus University
Department of Mathematical Sciences
http://www.imf.au.dk/~oebn/