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Overall, the book will help readers who want to learn modern analyti-cal tools for solving various applied problems of mathematical finance andphysics. From the mathematical perspective, the level of details is closer tothe applied rather than to the abstract or pure theoretical mathematics.The book could also be a subject of a semester course on integral trans-forms and their financial applications for Master and Ph.D. programs incomputational finance or financial engineering or, possibly, applied mathe-matics. It can also be used to train practitioners who want to extend theirknowledge of modern tools of mathematical and computational finance.
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Subjects
Numerical analysis, Finance, mathematical models, Probabilities., Stochastic processes, Integral transforms, Mathematical Statistics, financial mathematics, Markov processes, Stochastic partial differential equations, Partial Differential equations, Integral equations, Mathematical Economics, Special FunctionsShowing 1 featured edition. View all 1 editions?
Edition | Availability |
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1
Generalized Integral Transforms In Mathematical Finance
October 15, 2021, World Scientific Publishing Company Pte Ltd.
Hardcover
in English
- First edition
9811231737 9789811231735
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Book Details
Table of Contents
Edition Notes
Contains bibliography and index at pages 455 and 471 respectively. List of figures are provided at page xxvii.
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Work Description
This book describes several techniques, first invented in physics for solving problems of heat and mass transfer, and applies them to various problems of mathematical finance defined in domains with moving boundaries. These problems include:
(a) semi-closed form pricing of options in the one-factor models with time-dependent barriers (Bachelier, Hull-White, CIR, CEV);
(b) analyzing an interconnected banking system in the structural credit risk model with default contagion;
(c) finding first hitting time density for a reducible diffusion process;
(d) describing the exercise boundary of American options;
(e) calculating default boundary for the structured default problem;
(f) deriving a semi-closed form solution for optimal mean-reverting trading strategies; to mention but some.
The main methods used in this book are generalized integral transforms and heat potentials. To find a semi-closed form solution, we need to solve a linear or nonlinear Volterra equation of the second kind and then represent the option price as a one-dimensional integral. Our analysis shows that these methods are computationally more efficient than the corresponding finite-difference methods for the backward or forward Kolmogorov PDEs (partial differential equations) while providing better accuracy and stability. We extend a large number of known results by either providing solutions on complementary or extended domains where the solution is not known yet or modifying these techniques and applying them to new types of equations, such as the Bessel process. The book contains several novel results broadly applicable in physics, mathematics, and engineering.
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- Created October 1, 2022
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August 17, 2023 | Edited by ImportBot | import existing book |
November 15, 2022 | Edited by ImportBot | import existing book |
October 1, 2022 | Edited by Kaustubh Chakraborty | Added new book |
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October 1, 2022 | Created by Kaustubh Chakraborty | Added new book. |