Forward backward stochastic differential equations and their applications:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | German |
| Veröffentlicht: |
Berlin [u.a.]
Springer
1999
|
| Schriftenreihe: | Lecture notes in mathematics
1702 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 270 S. |
| ISBN: | 3540659609 |
Internformat
MARC
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| 100 | 1 | |a Ma, Jin |d 1956- |e Verfasser |0 (DE-588)121010988 |4 aut | |
| 245 | 1 | 0 | |a Forward backward stochastic differential equations and their applications |c Jin Ma ; Jiongmin Yong |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1999 | |
| 300 | |a XIII, 270 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in mathematics |v 1702 | |
| 650 | 7 | |a Algebra linear |2 larpcal | |
| 650 | 7 | |a Equacoes diferenciais |2 larpcal | |
| 650 | 7 | |a Stochastische differentiaalvergelijkingen |2 gtt | |
| 650 | 4 | |a Équations différentielles stochastiques | |
| 650 | 4 | |a Stochastic differential equations | |
| 650 | 0 | 7 | |a Optimale Kontrolle |0 (DE-588)4121428-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Stochastische Differentialgleichung |0 (DE-588)4057621-8 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Stochastische Differentialgleichung |0 (DE-588)4057621-8 |D s |
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| 689 | 1 | 0 | |a Optimale Kontrolle |0 (DE-588)4121428-6 |D s |
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| 700 | 1 | |a Yong, Jiongmin |d 1958- |e Verfasser |0 (DE-588)121010481 |4 aut | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-008518973 | ||
Datensatz im Suchindex
| _version_ | 1804127193019711488 |
|---|---|
| adam_text | Contents
Preface vii
Chapter 1. Introduction 1
§1. Some Examples 1
§1.1. A first glance 1
§1.2. A stochastic optimal control problem 3
§1.3. Stochastic differential utility 4
§1.4. Option pricing and contingent claim valuation 7
§2. Definitions and Notations 8
§3. Some Nonsolvable FBSDEs 10
§4. Well posedness of BSDEs 14
§5. Solvability of FBSDEs in Small Time Durations 19
§6. Comparison Theorems for BSDEs and FBSDEs 22
Chapter 2. Linear Equations 25
§1. Compatible Conditions for Solvability 25
§2. Some Reductions 30
§3. Solvability of Linear FBSDEs 33
§3.1. Necessary conditions 34
§3.2. Criteria for solvability 39
§4. A Riccati Type Equation 45
§5. Some Extensions 49
Chapter 3. Method of Optimal Control 51
§1. Solvability and the Associated Optimal Control Problem 51
§1.1. An optimal control problem 51
§1.2. Approximate Solvability 54
§2. Dynamic Programming Method and the HJB Equation 57
§3. The Value Function 60
§3.1. Continuity and semi concavity 60
§3.2. Approximation of the value function 64
§4. A Class of Approximately Solvable FBSDEs 69
§5. Construction of Approximate Adapted Solutions 75
Chapter 4. Four Step Scheme 80
§1. A Heuristic Derivation of Four Step Scheme 80
§2. Non Degenerate Case—Several Solvable Classes 84
§2.1. A general case 84
§2.2. The case when h has linear growth in z 86
§2.3. The case when m 1 88
§3. Infinite Horizon Case 89
xii Contents
§3.1. The nodal solution , 89
§3.2. Uniqueness of nodal solutions 92
§3.3. The limit of finite duration problems 98
Chapter 5. Linear, Degenerate Backward Stochastic
Partial Differential Equations 103
§1. Formulation of the Problem 103
§2. Well posedness of Linear BSPDEs 106
§3. Uniqueness of Adapted Solutions Ill
§3.1. Uniqueness of adapted weak solutions Ill
§3.2. An Ito formula 113
§4. Existence of Adapted Solutions 118
§5. A Proof of the Fundamental Lemma 126
§6. Comparison Theorems 130
Chapter 6. The Method of Continuation 137
§1. The Bridge 137
§2. Method of Continuation 140
§2.1. The solvability of FBSDEs linked by bridges 140
§2.2. A priori estimate 143
§3. Some Solvable FBSDEs 148
§3.1. A trivial FBSDE 148
§3.2. Decoupled FBSDEs 149
§3.3. FBSDEs with monotonicity conditions 151
§4. Properties of Bridges 154
§5. Construction of Bridges 158
§5.1. A general consideration 158
§5.2. A one dimensional case 161
Chapter 7. FBSDEs with Reflections 169
§1. Forward SDEs with Reflections 169
§2. Backward SDEs with Reflections 171
§3. Reflected Forward Backward SDEs 181
§3.1 A priori estimates 182
§3.2 Existence and uniqueness of the adapted solutions 186
§3.3 A continuous dependence result 190
Chapter 8. Applications of FBSDEs 193
§1. An Integral Representation Formula 193
§2. A Nonlinear Feynman Kac Formula 197
§3. Black s Consol Rate Conjecture 201
§4. Hedging Options for a Large Investor 207
§4.1. Hedging without constraint 210
§4.2. Hedging with constraint 219
§5. A Stochastic Black Scholes Formula 226
Contents xiii
§5.1. Stochastic Black Scholes formula 227
§5.2. The convexity of the European contingent claims 229
§5.3. The robustness of Black Scholes formula 231
§6. An American Game Option 232
Chapter 9. Numerical Methods for FBSDEs 235
§1. Formulation of the Problem 235
§2. Numerical Approximation of the Quasilinear PDEs 237
§2.1 A special case 237
§2.1.1. Numerical scheme 238
§2.1.2. Error analysis 240
§2.1.3. The approximating solutions {u(n)}£Li 244
§2.2 General case 245
§2.2.1. Numerical scheme 247
§2.2.2. Error analysis 248
§3. Numerical Approximation of the Forward SDE 250
Comments and Remarks 257
References 259
Index 269
|
| any_adam_object | 1 |
| author | Ma, Jin 1956- Yong, Jiongmin 1958- |
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| dewey-full | 510 519.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics 519 - Probabilities and applied mathematics |
| dewey-raw | 510 519.2 |
| dewey-search | 510 519.2 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV012544281 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:29:27Z |
| institution | BVB |
| isbn | 3540659609 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008518973 |
| oclc_num | 41315381 |
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| physical | XIII, 270 S. |
| publishDate | 1999 |
| publishDateSearch | 1999 |
| publishDateSort | 1999 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Ma, Jin 1956- Verfasser (DE-588)121010988 aut Forward backward stochastic differential equations and their applications Jin Ma ; Jiongmin Yong Berlin [u.a.] Springer 1999 XIII, 270 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1702 Algebra linear larpcal Equacoes diferenciais larpcal Stochastische differentiaalvergelijkingen gtt Équations différentielles stochastiques Stochastic differential equations Optimale Kontrolle (DE-588)4121428-6 gnd rswk-swf Stochastische Differentialgleichung (DE-588)4057621-8 gnd rswk-swf Stochastische Differentialgleichung (DE-588)4057621-8 s DE-604 Optimale Kontrolle (DE-588)4121428-6 s Yong, Jiongmin 1958- Verfasser (DE-588)121010481 aut Lecture notes in mathematics 1702 (DE-604)BV000676446 1702 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008518973&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ma, Jin 1956- Yong, Jiongmin 1958- Forward backward stochastic differential equations and their applications Lecture notes in mathematics Algebra linear larpcal Equacoes diferenciais larpcal Stochastische differentiaalvergelijkingen gtt Équations différentielles stochastiques Stochastic differential equations Optimale Kontrolle (DE-588)4121428-6 gnd Stochastische Differentialgleichung (DE-588)4057621-8 gnd |
| subject_GND | (DE-588)4121428-6 (DE-588)4057621-8 |
| title | Forward backward stochastic differential equations and their applications |
| title_auth | Forward backward stochastic differential equations and their applications |
| title_exact_search | Forward backward stochastic differential equations and their applications |
| title_full | Forward backward stochastic differential equations and their applications Jin Ma ; Jiongmin Yong |
| title_fullStr | Forward backward stochastic differential equations and their applications Jin Ma ; Jiongmin Yong |
| title_full_unstemmed | Forward backward stochastic differential equations and their applications Jin Ma ; Jiongmin Yong |
| title_short | Forward backward stochastic differential equations and their applications |
| title_sort | forward backward stochastic differential equations and their applications |
| topic | Algebra linear larpcal Equacoes diferenciais larpcal Stochastische differentiaalvergelijkingen gtt Équations différentielles stochastiques Stochastic differential equations Optimale Kontrolle (DE-588)4121428-6 gnd Stochastische Differentialgleichung (DE-588)4057621-8 gnd |
| topic_facet | Algebra linear Equacoes diferenciais Stochastische differentiaalvergelijkingen Équations différentielles stochastiques Stochastic differential equations Optimale Kontrolle Stochastische Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008518973&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
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