Generalized integral transforms in mathematical finance:
"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-f...
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| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore
World Scientific
2021
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | "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"-- |
| Beschreibung: | 1 Online-Ressource (508 Seiten) |
| ISBN: | 9789811231742 9811231745 |
| DOI: | 10.1142/12147 |
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| 520 | |a "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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Datensatz im Suchindex
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| dewey-ones | 650 - Management and auxiliary services |
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| discipline | Wirtschaftswissenschaften |
| discipline_str_mv | Wirtschaftswissenschaften |
| doi_str_mv | 10.1142/12147 |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
| index_date | 2024-07-03T18:44:41Z |
| indexdate | 2024-07-10T09:17:36Z |
| institution | BVB |
| isbn | 9789811231742 9811231745 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-033012175 |
| oclc_num | 1289775754 |
| open_access_boolean | |
| physical | 1 Online-Ressource (508 Seiten) |
| psigel | ZDB-124-WOP |
| publishDate | 2021 |
| publishDateSearch | 2021 |
| publishDateSort | 2021 |
| publisher | World Scientific |
| record_format | marc |
| spelling | Itkin, Andrey Verfasser aut Generalized integral transforms in mathematical finance Andrey Itkin, Alexander Lipton, Dmitry Muravey Singapore World Scientific 2021 1 Online-Ressource (508 Seiten) txt rdacontent c rdamedia cr rdacarrier "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"-- Business mathematics Integral transforms Electronic books Lipton, Alexander Sonstige oth Muravey, Dmitry Sonstige oth Erscheint auch als Druck-Ausgabe 9789811231735 Erscheint auch als Druck-Ausgabe 9811231737 https://doi.org/10.1142/12147 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Itkin, Andrey Generalized integral transforms in mathematical finance Business mathematics Integral transforms |
| title | Generalized integral transforms in mathematical finance |
| title_auth | Generalized integral transforms in mathematical finance |
| title_exact_search | Generalized integral transforms in mathematical finance |
| title_exact_search_txtP | Generalized integral transforms in mathematical finance |
| title_full | Generalized integral transforms in mathematical finance Andrey Itkin, Alexander Lipton, Dmitry Muravey |
| title_fullStr | Generalized integral transforms in mathematical finance Andrey Itkin, Alexander Lipton, Dmitry Muravey |
| title_full_unstemmed | Generalized integral transforms in mathematical finance Andrey Itkin, Alexander Lipton, Dmitry Muravey |
| title_short | Generalized integral transforms in mathematical finance |
| title_sort | generalized integral transforms in mathematical finance |
| topic | Business mathematics Integral transforms |
| topic_facet | Business mathematics Integral transforms |
| url | https://doi.org/10.1142/12147 |
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