Elementary calculus of financial mathematics:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Philadelphia, Pa.
Society for Industrial and Applied Mathematics
2009
|
| Schriftenreihe: | Mathematical modeling and computation
15 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | XII, 128 S. graph. Darst. |
| ISBN: | 9780898716672 |
Internformat
MARC
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| 020 | |a 9780898716672 |9 978-0-898716-67-2 | ||
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| 100 | 1 | |a Roberts, A. J. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Elementary calculus of financial mathematics |c A. J. Roberts |
| 264 | 1 | |a Philadelphia, Pa. |b Society for Industrial and Applied Mathematics |c 2009 | |
| 300 | |a XII, 128 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Mathematical modeling and computation |v 15 | |
| 500 | |a Includes bibliographical references and index | ||
| 650 | 0 | |a Finance / Mathematical models | |
| 650 | 0 | |a Stochastic processes | |
| 650 | 0 | |a Investments / Mathematics | |
| 650 | 0 | |a Calculus | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Calculus | |
| 650 | 4 | |a Finance |x Mathematical models | |
| 650 | 4 | |a Investments |x Mathematics | |
| 650 | 4 | |a Stochastic processes | |
| 650 | 0 | 7 | |a Finanzmathematik |0 (DE-588)4017195-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Stochastischer Prozess |0 (DE-588)4057630-9 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Finanzmathematik |0 (DE-588)4017195-4 |D s |
| 689 | 0 | 1 | |a Stochastischer Prozess |0 (DE-588)4057630-9 |D s |
| 689 | 0 | |5 DE-604 | |
| 830 | 0 | |a Mathematical modeling and computation |v 15 |w (DE-604)BV035421440 |9 15 | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-017040916 | ||
Datensatz im Suchindex
| _version_ | 1804138504380219392 |
|---|---|
| adam_text | Contents
Preface
ix
List of Algorithms
xi
1
Financial Indices Appear to Be Stochastic Processes
1
1.1
Brownian motion is also called a Wiener process
............ 3
1.2
Stochastic drift and volatility are unique
................ 9
1.3
Basic numerics simulate an SDE
.................... 14
1.4
A binomial lattice prices call option
................... 20
1.5
Summary
................................. 32
Exercises
..................................... 33
2
Ito s Stochastic Calculus Introduced
39
2.1
Multiplicative noise reduces exponential growth
............ 39
2.2
Ito s formula solves some SDEs
..................... 43
2.3
The Black-Scholes equation prices options accurately
......... 48
2.4
Summary
................................. 56
Exercises
..................................... 57
3
The Fokker-Planck Equation Describes the Probability Distribution
61
3.1
The probability distribution evolves forward in time
.......... 65
3.2
Stochastically solve deterministic differential equations
........ 76
3.3
The Kolmogorov backward equation completes the picture
...... 84
3.4
Summary
................................. 86
Exercises
..................................... 87
4
Stochastic Integration Proves Ito s Formula
93
4.1
The
Ito
integral
ƒ„
f
dW
......................... 95
4.2
The
Ito
formula
............................. 106
4.3
Summary
................................. 112
Exercises
..................................... 113
Appendix A Extra Matlab/Scilab Code
115
Appendix
В
Two Alternate Proofs
119
B.I Fokker-Planck equation
.........................119
vii
VIII
Contents
В.
2 Kolmogorov
backward equation
.....................121
Bibliography
125
Index
127
|
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| bvnumber | BV035235044 |
| callnumber-first | H - Social Science |
| callnumber-label | HG106 |
| callnumber-raw | HG106 |
| callnumber-search | HG106 |
| callnumber-sort | HG 3106 |
| callnumber-subject | HG - Finance |
| classification_rvk | QP 890 SK 980 |
| classification_tum | MAT 605f WIR 160f |
| ctrlnum | (OCoLC)258767971 (DE-599)GBV578741423 |
| dewey-full | 332.01/51923 |
| dewey-hundreds | 300 - Social sciences |
| dewey-ones | 332 - Financial economics |
| dewey-raw | 332.01/51923 |
| dewey-search | 332.01/51923 |
| dewey-sort | 3332.01 551923 |
| dewey-tens | 330 - Economics |
| discipline | Mathematik Wirtschaftswissenschaften |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T21:29:14Z |
| institution | BVB |
| isbn | 9780898716672 |
| language | English |
| lccn | 2008042349 |
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| physical | XII, 128 S. graph. Darst. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Society for Industrial and Applied Mathematics |
| record_format | marc |
| series | Mathematical modeling and computation |
| series2 | Mathematical modeling and computation |
| spelling | Roberts, A. J. Verfasser aut Elementary calculus of financial mathematics A. J. Roberts Philadelphia, Pa. Society for Industrial and Applied Mathematics 2009 XII, 128 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematical modeling and computation 15 Includes bibliographical references and index Finance / Mathematical models Stochastic processes Investments / Mathematics Calculus Mathematik Mathematisches Modell Finance Mathematical models Investments Mathematics Finanzmathematik (DE-588)4017195-4 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Finanzmathematik (DE-588)4017195-4 s Stochastischer Prozess (DE-588)4057630-9 s DE-604 Mathematical modeling and computation 15 (DE-604)BV035421440 15 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017040916&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Roberts, A. J. Elementary calculus of financial mathematics Mathematical modeling and computation Finance / Mathematical models Stochastic processes Investments / Mathematics Calculus Mathematik Mathematisches Modell Finance Mathematical models Investments Mathematics Finanzmathematik (DE-588)4017195-4 gnd Stochastischer Prozess (DE-588)4057630-9 gnd |
| subject_GND | (DE-588)4017195-4 (DE-588)4057630-9 |
| title | Elementary calculus of financial mathematics |
| title_auth | Elementary calculus of financial mathematics |
| title_exact_search | Elementary calculus of financial mathematics |
| title_full | Elementary calculus of financial mathematics A. J. Roberts |
| title_fullStr | Elementary calculus of financial mathematics A. J. Roberts |
| title_full_unstemmed | Elementary calculus of financial mathematics A. J. Roberts |
| title_short | Elementary calculus of financial mathematics |
| title_sort | elementary calculus of financial mathematics |
| topic | Finance / Mathematical models Stochastic processes Investments / Mathematics Calculus Mathematik Mathematisches Modell Finance Mathematical models Investments Mathematics Finanzmathematik (DE-588)4017195-4 gnd Stochastischer Prozess (DE-588)4057630-9 gnd |
| topic_facet | Finance / Mathematical models Stochastic processes Investments / Mathematics Calculus Mathematik Mathematisches Modell Finance Mathematical models Investments Mathematics Finanzmathematik Stochastischer Prozess |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017040916&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV035421440 |
| work_keys_str_mv | AT robertsaj elementarycalculusoffinancialmathematics |