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# đź“™ The Interval Market Model in Mathematical Finance: Game-Theoretic Methods by Pierre Bernhard, Jacob C. Engwerda, Berend Roorda, J.M. Schumacher, Vassili Kolokoltsov, Patrick Saint-Pierre, Jean-Pierre Aubin (auth.) â€” free pdf

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Toward the late 1990s, several research groups independently began developing new, related theories in mathematical finance. These theories did away with the standard stochastic geometric diffusion â€śSamuelsonâ€ť market model (also known as the Black-Scholes model because it is used in that most famous theory), instead opting for models that allowed minimax approaches to complement or replace stochastic methods. Among the most fruitful models were those utilizing game-theoretic tools and the so-called interval market model. Over time, these models have slowly but steadily gained influence in the financial community, providing a useful alternative to classical methods.

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Â· probability-free Black-Scholes theory;

Â· fair-price interval of an option;

Â· representation formulas and fast algorithms for option pricing;

Â· rainbow options;

Â· tychastic approach of mathematical finance based upon viability theory.

This book provides a welcome addition to the literature, complementing myriad titles on the market that take a classical approach to mathematical finance. It is a worthwhile resource for researchers in applied mathematics and quantitative finance, and has also been written in a manner accessible to financially-inclined readers with a limited technical background.

- Series:
**Static & Dynamic Game Theory: Foundations & Applications** - Author:
**Pierre Bernhard, Jacob C. Engwerda, Berend Roorda, J.M. Schumacher, Vassili Kolokoltsov, Patrick Saint-Pierre, Jean-Pierre Aubin (auth.)** - Year:
**2013** - Publisher:
**BirkhĂ¤user Basel** - Language:
**English** - ISBN:
**978-0-8176-8387-0,978-0-8176-8388-7**

- File size:
**3 812 102** - Format:
**pdf**

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This volume contains lectures delivered at the celebrated Seminar in Mathematical Finance at the Courant Institute. The lecturers and presenters of papers are prominent researchers and practitioners in the field of quantitative financial modelling. Most a...

Analysis, Geometry, and Modeling in Finance: Advanced Methods in Option Pricing is the first book that applies advanced analytical and geometrical methods used in physics and mathematics to the financial field. It even obtains new results when only appro...

In recent years, the theory has become widely accepted and has been further developed, but a detailed introduction is needed in order to make the material available and accessible to a wide audience. This will be the first book providing such an introduct...

Analysis, Geometry, and Modeling in Finance: Advanced Methods in Option Pricing is the first book that applies advanced analytical and geometrical methods used in physics and mathematics to the financial field. It even obtains new results when only approx...

Offering a unique balance between applications and calculations, Monte Carlo Methods and Models in Finance and Insurance incorporates the application background of finance and insurance with the theory and applications of Monte Carlo methods. It presents ...

The first in-depth analysis of inherent deficiencies in present practices â€śA book like this helps reduce the chance of a future breakdown in risk management.â€ť Professor Campbell R. Harvey, the Fuqua School of Business, Duke University ...

Offering a unique balance between applications and calculations, Monte Carlo Methods and Models in Finance and Insurance incorporates the application background of finance and insurance with the theory and applications of Monte Carlo methods. It presents ...

The year 2000 is the centenary year of the publication of Bachelier's thesis which - together with Harry Markovitz Ph.D. dissertation on portfolio selection in 1952 and Fischer Black's and Myron Scholes' solution of an option pricing problem in 1973 - is ...

Mathematical finance has grown into a huge area of research which requires a lot of care and a large number of sophisticated mathematical tools. Mathematically rigorous and yet accessible to advanced level practitioners and mathematicians alike, it consid...