The interval market model in mathematical finance game-theoretic methods Pierre Bernhard [and others]

Format:

Book

Contributor:

Bernhard, Pierre

Series:

Static & dynamic game theory

Language:

English

Subjects (All):

Business mathematics.

Game theory.

Game Theory.

Medical Subjects:

Game Theory.

Physical Description:

1 online resource

Place of Publication:

New York, NY Birkhäuser ©2013

Summary:

Toward the late 1990s, several research groups independently began developing new, related theories in mathematical finance. These theories didaway with the standard stochastic 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 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. 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

Contents:

Revisiting two classical results in dynamic portfolio management Merton's Optimal Dynamic Portfolio Revisited Option Pricing: Classic Results Hedging in Interval Models Introduction Fair Price Intervals Optimal Hedging Under Robust-Cost Constraints Appendix: Proofs Robust Control Approach to option Pricing Continuous and Discrete-Time Option Pricing and Interval Market Model Vanilla Options Digital Options Validation Game-theoretic analysis of rainbow options in incomplete markets Introduction Emergence of Risk-Neutral Probabilities from a Game-Theoretic Origin Rainbow Options in Discrete Time, I Rainbow Options in Discrete Time, II Continuous-Time Limits Credit Derivatives Viability Approach to Complex Options Pricing and Portfolio Insurance Computational Methods Based on the Guaranteed Capture Basin Algorithm Asset and Liability Insurance Management (ALIM) for Risk Eradication

Notes:

Includes bibliographical references and index

Other Format:

Print version Interval market model in mathematical finance

ISBN:

9780817683887

0817683887

OCLC:

823509025

Access Restriction:

Restricted for use by site license