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The Interval Market Model in Mathematical Finance: Game-Theoretic Methods
     

The Interval Market Model in Mathematical Finance: Game-Theoretic Methods

by Pierre Bernhard
 

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Toward the late 1990s, several research groups independently began developing new, related theories in mathematical finance.These theories didaway with the standard shastic geometric diffusion “Samuelson” 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

Overview

Toward the late 1990s, several research groups independently began developing new, related theories in mathematical finance.These theories didaway with the standard shastic geometric diffusion “Samuelson” 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 approachesto complement or replace shastic 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.

A self-contained monograph, The Interval Market Model in Mathematical Finance: Game-Theoretic Methodsassembles some of the most important results, old and new, in this area of research. Written by seven of the most prominent pioneers of the interval market model and game-theoretic finance, the work provides a detailed account of several closely relatedmodeling techniquesfor an array of problems in mathematical economics. The book isdivided into five parts, which successively address topics including:

· probability-free Black-Scholes theory;

· fair-price interval of an option;

· representation formulas and fast algorithms for option pricing;

· rainbow options;

· tychastic approach of mathematical finance based upon viability theory.

This book providesa welcome addition to the literature, complementing myriad titles on the market that take a classical approach to mathematical finance. Itis a worthwhile resource for researchers in applied mathematics and quantitative finance,and has also beenwritten in a manneraccessible to financially-inclined readers with a limited technical background.

Product Details

ISBN-13:
9780817683870
Publisher:
Springer New York
Publication date:
12/14/2012
Series:
Static & Dynamic Game Theory: Foundations & Applications Series
Edition description:
2013
Pages:
348
Product dimensions:
6.10(w) x 9.25(h) x 0.03(d)

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