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 approximate and partial solutions were previously available.
Through the problem of option pricing, the author introduces powerful tools and methods, including differential geometry, spectral decomposition, and supersymmetry, and applies these methods to practical problems in finance. He mainly focuses on the calibration and dynamics of implied volatility, which is commonly called smile. The book covers the Black-Scholes, local volatility, and stochastic volatility models, along with the Kolmogorov, Schrödinger, and Bellman-Hamilton-Jacobi equations.
Providing both theoretical and numerical results throughout, this book offers new ways of solving financial problems using techniques found in physics and mathematics.
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 approximate and partial solutions were previously available.
Through the problem of option pricing, the author introduces powerful tools and methods, including differential geometry, spectral decomposition, and supersymmetry, and applies these methods to practical problems in finance. He mainly focuses on the calibration and dynamics of implied volatility, which is commonly called smile. The book covers the Black-Scholes, local volatility, and stochastic volatility models, along with the Kolmogorov, Schrödinger, and Bellman-Hamilton-Jacobi equations.
Providing both theoretical and numerical results throughout, this book offers new ways of solving financial problems using techniques found in physics and mathematics.
The essays in this special volume survey some of the most recent advances in the global analysis of dynamic models for economics, finance and the social sciences. They deal in particular with a range...
This book includes selected papers presented at the MIMS (Mediterranean Institute for the Mathematical Sciences) - GGTM (Geometry and Topology Grouping for the Maghreb) conference, held in memory of...
In the past century, different branches of mathematics have become more widely separated. Yet, there is an essential unity to mathematics which still springs up in fascinating ways to solve...
At the heart of Clifford analysis is the study of systems of special partial differential operators that arise naturally from the use of Clifford algebra as a calculus tool. This book focuses on the...
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