The Brownian motion: a rigorous but gentle introduction for economists
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cham
Springer Open
[2019]
|
| Series: | Springer texts in business and economics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | x, 125 Seiten Diagramme |
| ISBN: | 9783030201029 |
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MARC
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Record in the Search Index
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| adam_text | 1 Introduction.................................................................................................. 1.1 Stochastics in Finance Theory............................................................ 1.2 Precision and Intuition in the Valuation of Derivatives..................... 1.3 Purpose of the Book............................................................................ 1 1 3 6 2 Set Theory..................................................................................................... 2.1 Notation and Set Operations................................................................. 2.2 Events and Sets...................................................................................... 15 15 20 3 Measures and Probabilities........................................................................ 3.1 Basic Problem of Measurement Theory ............................................. 3.2 σ-Algebras and Their Formal Definition ............................................ 3.3 Examples of Measurable Sets and Their Interpretation..................... 3.4 Further Examples: Infinite Number of States and Times................... 3.5 Definition of a Measure........................................................................ 3.6 Stieltjes Measure................................................................................... 3.7 Dirac Measure....................................................................................... 3.8 Null Sets and the Almost-Everywhere Property................................. 29 29 37 40 43 50 52 54 54 4 Random
Variables....................................................................................... 4.1 Random Variables as Functions........................................................... 4.2 Random Variables as Measurable Functions....................................... 4.3 Distribution Functions.......................................................................... 59 60 62 67 5 Expectation and Lebesgue Integral........................................................... 5.1 Definition of Expectation: A Problem ................................................ 5.2 Riemann Integral................................................................................... 5.3 Lebesgue Integral................................................................................. 5.4 Result: Expectation and Variance as Lebesgue Integral..................... 5.5 Conditional Expectation....................................................................... 69 69 70 71 80 80 6 Wiener’s Construction of the Brownian Motion...................................... 6.1 Preliminary Remark: The Space of All Paths..................................... 6.2 Wiener Measure on the Space of Continuous Functions................... 6.3 Two Definitions of the Brownian Motion............................................ 6.4 Often Neglected Properties of the Brownian Motion......................... 87 87 90 93 95 ix
x 7 Contents Supplements............................................................................................ 103 7.1 7.2 7.3 7.4 Cardinality of Sets................................................................................ Continuous and Almost Nowhere Differentiable Functions.............. Convergence Terms.............................................................................. Conditional Expectations Are Random Variables.............................. 103 107 110 115 References...................................................................................................... 121 Index.............................................................................................................. 123
|
| any_adam_object | 1 |
| author | Löffler, Andreas 1964- Kruschwitz, Lutz 1943- |
| author_GND | (DE-588)132421828 (DE-588)120168456 |
| author_facet | Löffler, Andreas 1964- Kruschwitz, Lutz 1943- |
| author_role | aut aut |
| author_sort | Löffler, Andreas 1964- |
| author_variant | a l al l k lk |
| building | Verbundindex |
| bvnumber | BV046079717 |
| classification_rvk | QH 150 QH 170 SK 820 |
| ctrlnum | (OCoLC)1113490864 (DE-599)BVBBV046079717 |
| discipline | Mathematik Wirtschaftswissenschaften |
| format | Book |
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| institution | BVB |
| isbn | 9783030201029 |
| language | English |
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| physical | x, 125 Seiten Diagramme |
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| publisher | Springer Open |
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| spelling | Löffler, Andreas 1964- Verfasser (DE-588)132421828 aut The Brownian motion a rigorous but gentle introduction for economists Andreas Löffler ; Lutz Kruschwitz Cham Springer Open [2019] x, 125 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Springer texts in business and economics Wirtschaftstheorie (DE-588)4079351-5 gnd rswk-swf Finanztheorie (DE-588)4154425-0 gnd rswk-swf Statistik (DE-588)4056995-0 gnd rswk-swf Finanztheorie (DE-588)4154425-0 s Wirtschaftstheorie (DE-588)4079351-5 s Statistik (DE-588)4056995-0 s 1\p DE-604 Kruschwitz, Lutz 1943- Verfasser (DE-588)120168456 aut Erscheint auch als Online-Ausgabe Löffler, Andreas, 1964- The Brownian motion 978-3-030-20103-6 (DE-604)BV046158249 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=031460842&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Löffler, Andreas 1964- Kruschwitz, Lutz 1943- The Brownian motion a rigorous but gentle introduction for economists Wirtschaftstheorie (DE-588)4079351-5 gnd Finanztheorie (DE-588)4154425-0 gnd Statistik (DE-588)4056995-0 gnd |
| subject_GND | (DE-588)4079351-5 (DE-588)4154425-0 (DE-588)4056995-0 |
| title | The Brownian motion a rigorous but gentle introduction for economists |
| title_auth | The Brownian motion a rigorous but gentle introduction for economists |
| title_exact_search | The Brownian motion a rigorous but gentle introduction for economists |
| title_full | The Brownian motion a rigorous but gentle introduction for economists Andreas Löffler ; Lutz Kruschwitz |
| title_fullStr | The Brownian motion a rigorous but gentle introduction for economists Andreas Löffler ; Lutz Kruschwitz |
| title_full_unstemmed | The Brownian motion a rigorous but gentle introduction for economists Andreas Löffler ; Lutz Kruschwitz |
| title_short | The Brownian motion |
| title_sort | the brownian motion a rigorous but gentle introduction for economists |
| title_sub | a rigorous but gentle introduction for economists |
| topic | Wirtschaftstheorie (DE-588)4079351-5 gnd Finanztheorie (DE-588)4154425-0 gnd Statistik (DE-588)4056995-0 gnd |
| topic_facet | Wirtschaftstheorie Finanztheorie Statistik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=031460842&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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