Lectures on BSDEs, Stochastic Control, and Stochastic Differential Games with Financial Applications:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | Englisch |
| Veröffentlicht: |
Philadelphia, Pa.
Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104)
2016
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| Schriftenreihe: | Financial Mathematics
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| Schlagwörter: | |
| Links: | http://epubs.siam.org/doi/book/10.1137/1.9781611974249 http://epubs.siam.org/doi/book/10.1137/1.9781611974249 https://doi.org/10.1137/1.9781611974249 http://epubs.siam.org/doi/book/10.1137/1.9781611974249 https://doi.org/10.1137/1.9781611974249 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029686239&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | 1 Online-Ressource |
| ISBN: | 9781611974249 |
| DOI: | 10.1137/1.9781611974249 |
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| adam_text | Titel: Lectures on BSDEs, stochastic control, and stochastic differential games with financial applications
Autor: Carmona, René
Jahr: 2016
RENÉCARMONA Princeton University Princeton, New Jersey Lectures on BSDEs, Stochastic Control, and Stochastic Differential Games with Financial Applications Siam.. Society for Industrial and Applied Mathematics Philadelphia
Contents Preface vii List of Notation ix I Stochastic Calculus Preliminaries 1 1 Stochastic Differential Equations 3 1.1 Notation and First Definitions...................... 3 1.2 Existence and Uniqueness of Strong Solutions: The Lipschitz Case . . 4 1.3 SDEs of McKean-Vlasov Type..................... 11 1.4 Conditional Propagation of Chaos.................... 18 1.5 Notes Complements..........................26 2 Backward Stochastic Differential Equations 27 2.1 Introduction and First Definitions....................27 2.2 Mean-Field BSDEs........................... 35 2.3 Reflected Backward Stochastic Differential Equations (RBSDEs) ... 37 2.4 Forward-Backward Stochastic Differential Equations (FBSDEs) .... 40 2.5 Existence and Uniqueness of Solutions.................46 2.6 The Affine Case.............................58 2.7 Notes Complements..........................63 II Stochastic Control 65 3 Continuous Time Stochastic Optimization and Control 67 3.1 Optimization of Stochastic Dynamical Systems............. 67 3.2 First Financial Applications.......................75 3.3 Dynamic Programming and the HJB Equation.............79 3.4 Infinite Horizon Case.......................... 85 3.5 Constraints and Singular Control Problems............... 87 3.6 Viscosity Solutions of HJB Equations and QVIs............101 3.7 Impulse Control Problems........................107 3.8 Ergodic Control.............................112 4 Probabilistic Approaches to Stochastic Control 119 4.1 BSDEs and Stochastic Control .....................119 4.2 Pontryagin Stochastic Maximum Principle...............125 4.3 Linear-Quadratic (LQ) Models.....................136 v
vi Contents 4.4 Optimal Control of McKean-Vlasov Dynamics ............141 4.5 Notes Complements..........................160 III Stochastic Differential Games 163 5 Stochastic Differential Games 165 5.1 Introduction and First Definitions....................165 5.2 Specific Examples............................176 5.3 Weak Formulation and the Case of Uncontrolled Volatility.......182 5.4 Game Versions of the Stochastic Maximum Principle .........186 5.5 A Simple Model for Systemic Risk...................198 5.6 A Predatory Trading Game Model ...................204 5.7 Notes Complements..........................216 6 Mean-Field Games 219 6.1 Introduction and First Definitions....................219 6.2 A Full Solution Without the Common Noise..............226 6.3 Propagation of Chaos and Approximate Nash Equilibriums......236 6.4 Applications and Open Problems....................243 6.5 Notes Complements..........................250 Bibliography 253 Author Index 261 Subject Index 263
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| indexdate | 2024-12-20T17:58:45Z |
| institution | BVB |
| isbn | 9781611974249 |
| language | English |
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| spellingShingle | Carmona, René 1947- Lectures on BSDEs, Stochastic Control, and Stochastic Differential Games with Financial Applications Stochastische Analysis (DE-588)4132272-1 gnd Stochastische optimale Kontrolle (DE-588)4207850-7 gnd Differentialspiel (DE-588)4012253-0 gnd |
| subject_GND | (DE-588)4132272-1 (DE-588)4207850-7 (DE-588)4012253-0 |
| title | Lectures on BSDEs, Stochastic Control, and Stochastic Differential Games with Financial Applications |
| title_auth | Lectures on BSDEs, Stochastic Control, and Stochastic Differential Games with Financial Applications |
| title_exact_search | Lectures on BSDEs, Stochastic Control, and Stochastic Differential Games with Financial Applications |
| title_full | Lectures on BSDEs, Stochastic Control, and Stochastic Differential Games with Financial Applications René Carmona |
| title_fullStr | Lectures on BSDEs, Stochastic Control, and Stochastic Differential Games with Financial Applications René Carmona |
| title_full_unstemmed | Lectures on BSDEs, Stochastic Control, and Stochastic Differential Games with Financial Applications René Carmona |
| title_short | Lectures on BSDEs, Stochastic Control, and Stochastic Differential Games with Financial Applications |
| title_sort | lectures on bsdes stochastic control and stochastic differential games with financial applications |
| topic | Stochastische Analysis (DE-588)4132272-1 gnd Stochastische optimale Kontrolle (DE-588)4207850-7 gnd Differentialspiel (DE-588)4012253-0 gnd |
| topic_facet | Stochastische Analysis Stochastische optimale Kontrolle Differentialspiel |
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