[Sem-coll] AM Sem/Coll April 23 [Taskar], April 24 [Moffit], April 25 [Bielecki]

Robert Ellis rellis at math.iit.edu
Mon Apr 23 15:06:50 CDT 2007


My apologies for the multiple announcements.  We recently obtained the 
abstract for Steven Moffitt's Tuesday talk (2nd listing below), which has 
not yet been mailed to everyone.

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AM colloqium: Monday, April 23, 4:40pm E1 106
Speaker: Michael Taksar (University of Missouri-Columbia)
Title: Singular stochastic control and related pdes with gradient
constraints in portfolio optimization models in mathematical finance
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AM seminar Tuesday, April 24 3:30pm E1 242
Speaker: Steven Moffit (W.H. Trading, LLC)
Title: Tsallis Statistics - A New Paradigm In Statistical Mechanics With
Applications in Finance


Abstract

A new formalism in statistical mechanics, that of the nonextensive 
statistical mechanics (NESM), was proposed in 1998 by physicist 
Constantino Tsallis. Although NESM remains controversial, it has generated 
considerable research interest due to its success in describing systems 
that do not obey Boltzmann-Gibbs statistice. To date there are over 2000 
publications on Tsallis statistics, including over 80 in the areas of 
finance and time series.

Following an overview of the emerging field of econophysics, the Tsallis 
approach will be introduced incrementally. First, a brief review of 
classical statistical mechanics that references the work of 
Maxwell-Boltzmann, Shannon and Jaynes is given. Next, the maximum entropy 
principle is stated, and its connection with the standard Brownian motion 
is given. Several examples of experimental and observational data are 
offered as evidence that a classical application of Boltzmann-Gibbs fails. 
Tsallis nonextensive statistics are then introduced. Since one of the main 
criticisms against the Tsallis statistics is that there are no physical 
models showing how they might arise, four etiological models are 
discussed:
(1) the Bening-Korolev nonextensive limit theorem,
(2) the Beck model of turbulence,
(3) the dynamic correlations model of Kodama, et. al. and
(4) the Lambiotte-Ausloos fluctuating mass model. A brief discussion of 
applications of NESM to stock price movement and options pricing concludes 
the discussion.
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AM colloquium Wednesday, April 25 4:40pm E1 242
Speaker: Luca Vidozzi (IIT Applied Mathematics)
Title: Markov Copulae and applications in finance
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