Exponential Functionals of Brownian Motion and Related Processes:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
2001
|
| Schriftenreihe: | Springer Finance
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | This monograph contains: - ten papers written by the author, and co-authors, between December 1988 and October 1998 about certain exponential functionals of Brownian motion and related processes, which have been, and still are, of interest, during at least the last decade, to researchers in Mathematical finance; - an introduction to the subject from the view point of Mathematical Finance by H. Geman. The origin of my interest in the study of exponentials of Brownian motion in relation with mathematical finance is the question, first asked to me by S. Jacka in Warwick in December 1988, and later by M. Chesney in Geneva, and H. Geman in Paris, to compute the price of Asian options, i. e. : to give, as much as possible, an explicit expression for: (1) where A~v) = I~ dsexp2(Bs + liS), with (Bs,s::::: 0) a real-valued Brownian motion. Since the exponential process of Brownian motion with drift, usually called: geometric Brownian motion, may be represented as: t ::::: 0, (2) where (Rt), u ::::: 0) denotes a 15-dimensional Bessel process, with 5 = 2(1I+1), it seemed clear that, starting from (2) [which is analogous to Feller's repre sentation of a linear diffusion X in terms of Brownian motion, via the scale function and the speed measure of X], it should be possible to compute quan tities related to (1), in particular: in hinging on former computations for Bessel processes |
| Beschreibung: | 1 Online-Ressource (IX, 205p) |
| ISBN: | 9783642566349 9783540659433 |
| ISSN: | 1616-0533 |
| DOI: | 10.1007/978-3-642-56634-9 |
Internformat
MARC
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Datensatz im Suchindex
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| isbn | 9783642566349 9783540659433 |
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| spelling | Yor, Marc Verfasser aut Exponential Functionals of Brownian Motion and Related Processes by Marc Yor Berlin, Heidelberg Springer Berlin Heidelberg 2001 1 Online-Ressource (IX, 205p) txt rdacontent c rdamedia cr rdacarrier Springer Finance 1616-0533 This monograph contains: - ten papers written by the author, and co-authors, between December 1988 and October 1998 about certain exponential functionals of Brownian motion and related processes, which have been, and still are, of interest, during at least the last decade, to researchers in Mathematical finance; - an introduction to the subject from the view point of Mathematical Finance by H. Geman. The origin of my interest in the study of exponentials of Brownian motion in relation with mathematical finance is the question, first asked to me by S. Jacka in Warwick in December 1988, and later by M. Chesney in Geneva, and H. Geman in Paris, to compute the price of Asian options, i. e. : to give, as much as possible, an explicit expression for: (1) where A~v) = I~ dsexp2(Bs + liS), with (Bs,s::::: 0) a real-valued Brownian motion. Since the exponential process of Brownian motion with drift, usually called: geometric Brownian motion, may be represented as: t ::::: 0, (2) where (Rt), u ::::: 0) denotes a 15-dimensional Bessel process, with 5 = 2(1I+1), it seemed clear that, starting from (2) [which is analogous to Feller's repre sentation of a linear diffusion X in terms of Brownian motion, via the scale function and the speed measure of X], it should be possible to compute quan tities related to (1), in particular: in hinging on former computations for Bessel processes Mathematics Finance Distribution (Probability theory) Probability Theory and Stochastic Processes Quantitative Finance Mathematik Finanzmathematik (DE-588)4017195-4 gnd rswk-swf Brownsche Bewegung (DE-588)4128328-4 gnd rswk-swf Stochastische Analysis (DE-588)4132272-1 gnd rswk-swf Stochastisches Modell (DE-588)4057633-4 gnd rswk-swf 1\p (DE-588)4143413-4 Aufsatzsammlung gnd-content Finanzmathematik (DE-588)4017195-4 s Stochastisches Modell (DE-588)4057633-4 s Brownsche Bewegung (DE-588)4128328-4 s 2\p DE-604 Stochastische Analysis (DE-588)4132272-1 s 3\p DE-604 https://doi.org/10.1007/978-3-642-56634-9 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Yor, Marc Exponential Functionals of Brownian Motion and Related Processes Mathematics Finance Distribution (Probability theory) Probability Theory and Stochastic Processes Quantitative Finance Mathematik Finanzmathematik (DE-588)4017195-4 gnd Brownsche Bewegung (DE-588)4128328-4 gnd Stochastische Analysis (DE-588)4132272-1 gnd Stochastisches Modell (DE-588)4057633-4 gnd |
| subject_GND | (DE-588)4017195-4 (DE-588)4128328-4 (DE-588)4132272-1 (DE-588)4057633-4 (DE-588)4143413-4 |
| title | Exponential Functionals of Brownian Motion and Related Processes |
| title_auth | Exponential Functionals of Brownian Motion and Related Processes |
| title_exact_search | Exponential Functionals of Brownian Motion and Related Processes |
| title_full | Exponential Functionals of Brownian Motion and Related Processes by Marc Yor |
| title_fullStr | Exponential Functionals of Brownian Motion and Related Processes by Marc Yor |
| title_full_unstemmed | Exponential Functionals of Brownian Motion and Related Processes by Marc Yor |
| title_short | Exponential Functionals of Brownian Motion and Related Processes |
| title_sort | exponential functionals of brownian motion and related processes |
| topic | Mathematics Finance Distribution (Probability theory) Probability Theory and Stochastic Processes Quantitative Finance Mathematik Finanzmathematik (DE-588)4017195-4 gnd Brownsche Bewegung (DE-588)4128328-4 gnd Stochastische Analysis (DE-588)4132272-1 gnd Stochastisches Modell (DE-588)4057633-4 gnd |
| topic_facet | Mathematics Finance Distribution (Probability theory) Probability Theory and Stochastic Processes Quantitative Finance Mathematik Finanzmathematik Brownsche Bewegung Stochastische Analysis Stochastisches Modell Aufsatzsammlung |
| url | https://doi.org/10.1007/978-3-642-56634-9 |
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