The Interval Market Model In Mathematical Finance Gametheoretic Methods

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Toward the late 1990s, various research groups began developing new theories in mathematical finance that moved away from the traditional stochastic geometric diffusion market model, often associated with the Black-Scholes theory. These new models incorporated minimax approaches and utilized game-theoretic tools, including the interval market model, which have gained traction within the financial community as viable alternatives to classical methods. This self-contained monograph assembles significant results in this field, authored by seven leading pioneers of the interval market model and game-theoretic finance. The work provides a comprehensive overview of various modeling techniques applicable to mathematical economics. It is organized into five parts covering topics such as probability-free Black-Scholes theory, fair-price intervals of options, representation formulas and algorithms for option pricing, rainbow options, and the tychastic approach based on viability theory. This book enriches the existing literature by offering a fresh perspective on mathematical finance, making it a valuable resource for researchers in applied mathematics and quantitative finance, while also being accessible to readers with a limited technical background.