Ett informationsblad från matematiska institutionen vid Linköpings universitet. Material till Lite Mat lämnas till Maud Lindström litemat@mai.liu.se senast torsdagar kl 12.00.

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***LITE MAT***

Ett informationsblad från matematiska institutionen vid Linköpings universitet

v14 2004

Matematiska kollokviet

Onsdagen den 31 mars, kl. 13.00-14.00 talar Prof. José M. M. Senovilla, University of the Basque Country, Bilbao,

Trapped submanifolds in Lorentzian geometry

Sammanfattning: In Lorentzian geometry, the concept of trapped submanifold will be introduced by means of the properties of the mean curvature vector. Trapped submanifolds are generalizations of the standard maximal hypersurfaces and minimal surfaces, of geodesics, and also of the trapped surfaces introduced by Penrose. Examples and selected applications to gravitational theories will be presented.

Onsdagen den 7 april, kl. 13.00-14.00 talar Vladimir Kozlov,

Zeros of eigenfunctions

Sammanfattning: It is known, that the nth eigenfunction, n = 0, 1, ..., to the second order Sturm-Liouville ordinary differential operator on an interval has exactly n zeros. I intend to discuss what is known about multi-dimensional problems and to present some new results.

Lokal: ISY/MAI:s seminarierum Glashuset, ing 25.

Välkomna!
Vladimir Kozlov,
Svante Linusson och
Stefan Rauch-Wojciechowski

Seminarium i matematisk statistik

Onsdagen den 31 mars, kl. 15.15 - 17.00 talar Prof.  Michael Sørensen, Department of Applied Mathematics and Statistics, University of Copenhagen,

Flexible classes of diffusion-type processes with a view to stochastic volatility models

Sammanfattning: Flexible stationary diffusion-type models are presented that can fit both the marginal distribution and the correlation structure found in many time series from e.g. finance and turbulence. Diffusion models with linear drift and a known and pre-specified marginal distribution are discussed, and the diffusion coefficients corresponding many commonly used probability distributions are given explicitly. An approximation to the diffusion coefficient based on saddlepoint approximation techniques is presented. The approximation is useful in cases where there is no explicit expression for the diffusion coefficient.
More general models are obtained as sums of diffusions with linear drift, for which the autocorrelation function is a convex combination of exponential functions. It is demonstrated theoretically as well as in an study of turbulence data that such models can fit quite complex correlation structures. Any infinitely divisible distribution satisfying a weak regularity condition can be obtained as marginal distribution.
To obtain an even more complex autocorrelation structure, it is necessary to use multidimensional diffusions with linear drift as building blocks. These models, that are of interest in their own right, can be used to construct one-dimensional processes with negative autocorrelation.
The processes presented in the talk can be used to model the volatility in a stochastic volatility model and thus obtain models driven purely by Wiener processes with properties similar to the stochastic volatility models driven partly by Levy processes with jumps proposed by Barndorff-Nielsen and Shephard. Particular examples are volatility processes with gamma distributed and the inverse Gaussian distributed marginal distributions, for which the returns are approximately variance-gamma distributed and normal inverse Gaussian (NIG) distributed, respectively. The fact that these models are Wiener driven makes discussion of derivative pricing straightforward.
The lecture is based on joint work with Bo Bibby, Ib Skovgaard and Martin Jacobsen.

Lokal: ISY/MAI:s seminarierum Glashuset, ing 25

Välkomna !
Timo Koski
Information: tikos@mai.liu.se, tfn: 28 1454

Presentation av examensarbete

Fredagen den 26 mars kl. 10-11 presenterar Fredric Helmfrid och Johan Westring sitt examensarbete

Agent Based Computational economics - A Multi-Agent Approach to Financial Markets.

Abstract: Asset prices are traditionally modeled by fitting stochastic processes to historic data. In this thesis another approach is taken. By developing an agent-based model asset prices arises from the interaction between a large number of agents. Our model consists of three types of agents: fundamental-, trend- and zero intelligence agents, who trade on a market similar to the Stockholm Stock Exchange. We show that our agent-based model manages to produce various important stylized facts e.g. fat tails and volatility clusters. Measures of the Hurst exponent on the data emanating from our model indicate that long memory effects exist in asset prices for all types of agents. Furthermore we explain the important role that individual risk preferences play in a closed financial market, and how the risk preferences are connected with asset prices. We conclude that agent-based models are powerful tools to understand the physical nature of markets and investors. There is still much work to do in the agent-based computational economics area, though we believe that agent-based models in conjunction with today's econometric knowledge can give further insight into the world of finance.

Lokal: ISY/MAI:s seminarierum Glashuset

Välkomna!
Jörgen Blomvall

Mer information om MAI finns på MAIs hemsida.
Material till Lite Mat lämnas till Maud Lindström senast torsdagar kl 12.00.
Tel 013-281405, Fax 013-149403, Email: litemat@mai.liu.se.