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Beschreibung
In World Mathematical Year 2000 the traditional St. Flour Summer School was hosted jointly with the European Mathematical Society. Sergio Albeverio reviews the theory of Dirichlet forms, and gives applications including partial differential equations, stochastic dynamics of quantum systems, quantum fields and the geometry of loop spaces. The second text, by Walter Schachermayer, is an introduction to the basic concepts of mathematical finance, including the Bachelier and Black-Scholes models. The fundamental theorem of asset pricing is discussed in detail. Finally Michel Talagrand, gives an overview of the mean field models for spin glasses. This text is a major contribution towards the proof of certain results from physics, and includes a discussion of the Sherrington-Kirkpatrick and the p-spin interaction models.
In World Mathematical Year 2000 the traditional St. Flour Summer School was hosted jointly with the European Mathematical Society. Sergio Albeverio reviews the theory of Dirichlet forms, and gives applications including partial differential equations, stochastic dynamics of quantum systems, quantum fields and the geometry of loop spaces. The second text, by Walter Schachermayer, is an introduction to the basic concepts of mathematical finance, including the Bachelier and Black-Scholes models. The fundamental theorem of asset pricing is discussed in detail. Finally Michel Talagrand, gives an overview of the mean field models for spin glasses. This text is a major contribution towards the proof of certain results from physics, and includes a discussion of the Sherrington-Kirkpatrick and the p-spin interaction models.
Zusammenfassung
Walter Schachermeyer, born in 1950 in Linz, Austria, has received--as the first mathematician--the 1998 Wittgenstein Award, Austria's highest honor for scienctific achievement. Since 1998 he holds the Chair for Actuarial and Financial Mathematics at the Vienna University of Technolgoy. Among his achievements is the proof of the "Fundamental Theorem of Asset Pricing" in its general form, which was done in joint work with Freddy Delbaen.Freddy Delbaen, born in 1946 in Duffel/Antwerpen, Belgium, is Professor for Financial Mathematics at the ETH in Zurich since 1995.
Inhaltsverzeichnis
Sergio Albeverio: Theory of Dirichlet forms and applications.- Functional analytic background: semigroups, generators, resolvents.- Closed symmetric coercive forms associated with Co-contraction semigroups.- Contraction properties of forms, positivity preserving and submarkovian semigroups.- Potential Theory and Markov Processes associated with Dirichlet Forms.- Diffusions and stochastic differential equations associated with classical Dirichlet forms.- Applications.- Walter Schachermayer: Introduction to the Mathematics of Financial Markets.- Introduction: Bachelier's Thesis from 1900.- Models of Financial Markets on Finite Probability Spaces.- The Binomial Model, Bachelier's Model and the Black-Scholes Model.- The No-Arbitrage Theory for General Processes.- Some Applications of the Fundamental Theorem of Asset Pricing.- Michel Talagrand: Mean field models for spin glasses: a first course.- What this is all about: the REM.- The Sherrington-Kirkpatrick model at high temperature.- The p-spin interaction model.- External field and the replica-symmetric solution.- Exponential inequalities.- Central limit theorems and the Almeida-Thouless line.- Emergence and separation of the lumps in the p-spin interaction model.
Details
| Erscheinungsjahr: | 2003 |
|---|---|
| Fachbereich: | Wahrscheinlichkeitstheorie |
| Genre: | Mathematik, Medizin, Naturwissenschaften, Technik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Taschenbuch |
| Reihe: | Lecture Notes in Mathematics |
| Inhalt: | Einband - flex.(Paperback) |
| ISBN-13: | 9783540403357 |
| ISBN-10: | 3540403353 |
| Sprache: | Englisch |
| Einband: | Kartoniert / Broschiert |
| Autor: |
Albeverio, Sergio
Schachermayer, Walter |
| Redaktion: | Bernard, Pierre |
| Hersteller: |
Springer
Lecture Notes in Mathematics |
| Verantwortliche Person für die EU: | Springer Nature Customer Service Center GmbH, Europaplatz 3, D-69115 Heidelberg, productsafety@springernature.com |
| Maße: | 235 x 155 x 17 mm |
| Von/Mit: | Sergio Albeverio (u. a.) |
| Erscheinungsdatum: | 14.07.2003 |
| Gewicht: | 0,47 kg |