Elementary stochastic calculus with finance in view:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Singapore [u.a.]
World Scientific
2000
|
| Ausgabe: | Reprint. |
| Schriftenreihe: | Advanced series on statistical science & applied probability
6 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | IX, 212 S. graph. Darst. |
| ISBN: | 9810235437 |
Internformat
MARC
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| 245 | 1 | 0 | |a Elementary stochastic calculus with finance in view |c Thomas Mikosch |
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| 300 | |a IX, 212 S. |b graph. Darst. | ||
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| 490 | 1 | |a Advanced series on statistical science & applied probability |v 6 | |
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents
Reader Guidelines 1
1 Preliminaries 5
1.1 Basic Concepts from Probability Theory 6
1.1.1 Random Variables 6
1.1.2 Random Vectors 14
1.1.3 Independence and Dependence 19
1.2 Stochastic Processes 23
1.3 Brownian Motion 33
1.3.1 Denning Properties 33
1.3.2 Processes Derived from Brownian Motion 40
1.3.3 Simulation of Brownian Sample Paths 44
1.4 Conditional Expectation 56
1.4.1 Conditional Expectation under Discrete Condition ... 56
1.4.2 About a Fields 62
1.4.3 The General Conditional Expectation 67
1.4.4 Rules for the Calculation of Conditional Expectations . 70
1.4.5 The Projection Property of Conditional Expectations . 74
1.5 Martingales 77
1.5.1 Defining Properties 77
1.5.2 Examples 81
1.5.3 The Interpretation of a Martingale as a Fair Game ... 84
2 The Stochastic Integral 87
2.1 The Riemann and Riemann Stieltjes Integrals 88
2.1.1 The Ordinary Riemann Integral 88
2.1.2 The Riemann Stieltjes Integral 92
2.2 The Ito Integral 96
2.2.1 A Motivating Example 96
viii CONTENTS
2.2.2 The Ito Stochastic Integral for Simple Processes .... 101
2.2.3 The General Ito Stochastic Integral 107
2.3 The Ito Lemma 112
2.3.1 The Classical Chain Rule of Differentiation 113
2.3.2 A Simple Version of the Ito Lemma 114
2.3.3 Extended Versions of the Ito Lemma 117
2.4 The Stratonovich and Other Integrals 123
3 Stochastic Differential Equations 131
3.1 Deterministic Differential Equations 132
3.2 Ito Stochastic Differential Equations 134
3.2.1 What is a Stochastic Differential Equation? 134
3.2.2 Solving Ito Stochastic Differential Equations by the Ito
Lemma 138
3.2.3 Solving Ito Differential Equations via Stratonovich Cal¬
culus 145
3.3 The General Linear Differential Equation 150
3.3.1 Linear Equations with Additive Noise 150
3.3.2 Homogeneous Equations with Multiplicative Noise . . . 153
3.3.3 The General Case 155
3.3.4 The Expectation and Variance Functions of the Solution 156
3.4 Numerical Solution 157
3.4.1 The Euler Approximation 158
3.4.2 The Milstein Approximation 162
4 Applications of Stochastic Calculus in Finance 167
4.1 The Black Scholes Option Pricing Formula 168
4.1.1 A Short Excursion into Finance 168
4.1.2 What is an Option? 170
4.1.3 A Mathematical Formulation of the Option Pricing Pro¬
blem 172
4.1.4 The Black and Scholes Formula 174
4.2 A Useful Technique: Change of Measure 176
4.2.1 What is a Change of the Underlying Measure? 176
4.2.2 An Interpretation of the Black Scholes Formula by Chan¬
ge of Measure 180
Appendix 185
Al Modes of Convergence 185
A2 Inequalities 187
CONTENTS ix
A3 Non Differentiability and Unbounded Variation of Brownian Sam¬
ple Paths 188
A4 Proof of the Existence of the General Ito Stochastic Integral . . 190
A5 The Radon Nikodym Theorem 193
A6 Proof of the Existence and Uniqueness of the Conditional Ex¬
pectation 194
Bibliography 195
Index 199
List of Abbreviations and Symbols 209
|
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| id | DE-604.BV012878320 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:35:21Z |
| institution | BVB |
| isbn | 9810235437 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008766131 |
| oclc_num | 248335845 |
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| physical | IX, 212 S. graph. Darst. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | World Scientific |
| record_format | marc |
| series | Advanced series on statistical science & applied probability |
| series2 | Advanced series on statistical science & applied probability |
| spelling | Mikosch, Thomas Verfasser aut Elementary stochastic calculus with finance in view Thomas Mikosch Reprint. Singapore [u.a.] World Scientific 2000 IX, 212 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Advanced series on statistical science & applied probability 6 Finanzmathematik - Stochastische Analysis Stochastische Analysis (DE-588)4132272-1 gnd rswk-swf Finanzmathematik (DE-588)4017195-4 gnd rswk-swf Finanzwirtschaft (DE-588)4017214-4 gnd rswk-swf Stochastische Analysis (DE-588)4132272-1 s Finanzwirtschaft (DE-588)4017214-4 s DE-604 Finanzmathematik (DE-588)4017195-4 s DE-188 Advanced series on statistical science & applied probability 6 (DE-604)BV011932321 6 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008766131&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mikosch, Thomas Elementary stochastic calculus with finance in view Advanced series on statistical science & applied probability Finanzmathematik - Stochastische Analysis Stochastische Analysis (DE-588)4132272-1 gnd Finanzmathematik (DE-588)4017195-4 gnd Finanzwirtschaft (DE-588)4017214-4 gnd |
| subject_GND | (DE-588)4132272-1 (DE-588)4017195-4 (DE-588)4017214-4 |
| title | Elementary stochastic calculus with finance in view |
| title_auth | Elementary stochastic calculus with finance in view |
| title_exact_search | Elementary stochastic calculus with finance in view |
| title_full | Elementary stochastic calculus with finance in view Thomas Mikosch |
| title_fullStr | Elementary stochastic calculus with finance in view Thomas Mikosch |
| title_full_unstemmed | Elementary stochastic calculus with finance in view Thomas Mikosch |
| title_short | Elementary stochastic calculus with finance in view |
| title_sort | elementary stochastic calculus with finance in view |
| topic | Finanzmathematik - Stochastische Analysis Stochastische Analysis (DE-588)4132272-1 gnd Finanzmathematik (DE-588)4017195-4 gnd Finanzwirtschaft (DE-588)4017214-4 gnd |
| topic_facet | Finanzmathematik - Stochastische Analysis Stochastische Analysis Finanzmathematik Finanzwirtschaft |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008766131&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV011932321 |
| work_keys_str_mv | AT mikoschthomas elementarystochasticcalculuswithfinanceinview |