Optimal stochastic control, stochastic target problems, and backward SDE:
Gespeichert in:
1. Verfasser: | |
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Format: | Elektronisch E-Book |
Sprache: | English |
Veröffentlicht: |
New York [u.a.]
Springer
2013
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Schriftenreihe: | Fields Institute monographs
29 |
Schlagworte: | |
Online-Zugang: | BTU01 TUM01 UBA01 UBM01 UBT01 UBW01 UPA01 Volltext Inhaltsverzeichnis Abstract |
Beschreibung: | 1 Online-Ressource (X, 214 S.) |
ISBN: | 1461442850 9781461442868 |
DOI: | 10.1007/978-1-4614-4286-8 |
Internformat
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Datensatz im Suchindex
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adam_text | OPTIMAL STOCHASTIC CONTROL, STOCHASTIC TARGET PROBLEMS, AND BACKWARD SDE
/ TOUZI, NIZAR
: 2013
TABLE OF CONTENTS / INHALTSVERZEICHNIS
PREFACE
1. CONDITIONAL EXPECTATION AND LINEAR PARABOLIC PDES
2. STOCHASTIC CONTROL AND DYNAMIC PROGRAMMING
3. OPTIMAL STOPPING AND DYNAMIC PROGRAMMING
4. SOLVING CONTROL PROBLEMS BY VERIFICATION
5. INTRODUCTION TO VISCOSITY SOLUTIONS
6. DYNAMIC PROGRAMMING EQUATION IN THE VISCOSITY SENSE
7. STOCHASTIC TARGET PROBLEMS
8. SECOND ORDER STOCHASTIC TARGET PROBLEMS
9. BACKWARD SDES AND STOCHASTIC CONTROL
10. QUADRATIC BACKWARD SDES
11. PROBABILISTIC NUMERICAL METHODS FOR NONLINEAR PDES
12. INTRODUCTION TO FINITE DIFFERENCES METHODS
REFERENCES
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
OPTIMAL STOCHASTIC CONTROL, STOCHASTIC TARGET PROBLEMS, AND BACKWARD SDE
/ TOUZI, NIZAR
: 2013
ABSTRACT / INHALTSTEXT
THIS BOOK COLLECTS SOME RECENT DEVELOPMENTS IN STOCHASTIC CONTROL THEORY
WITH APPLICATIONS TO FINANCIAL MATHEMATICS. IN THE FIRST PART OF THE
VOLUME, STANDARD STOCHASTIC CONTROL PROBLEMS ARE ADDRESSED FROM THE
VIEWPOINT OF THE RECENTLY DEVELOPED WEAK DYNAMIC PROGRAMMING PRINCIPLE.
A SPECIAL EMPHASIS IS PUT ON REGULARITY ISSUES AND, IN PARTICULAR, ON
THE BEHAVIOR OF THE VALUE FUNCTION NEAR THE BOUNDARY. THEN A QUICK
REVIEW OF THE MAIN TOOLS FROM VISCOSITY SOLUTIONS ALLOWING ONE TO
OVERCOME ALL REGULARITY PROBLEMS IS PROVIDED. THE SECOND PART IS
DEVOTED TO THE CLASS OF STOCHASTIC TARGET PROBLEMS, WHICH EXTENDS IN A
NONTRIVIAL WAY THE STANDARD STOCHASTIC CONTROL PROBLEMS. HERE THE THEORY
OF VISCOSITY SOLUTIONS PLAYS A CRUCIAL ROLE IN THE DERIVATION OF THE
DYNAMIC PROGRAMMING EQUATION AS THE INFINITESIMAL COUNTERPART OF THE
CORRESPONDING GEOMETRIC DYNAMIC PROGRAMMING EQUATION.THE VARIOUS
DEVELOPMENTS OF THIS THEORY HAVE BEEN STIMULATED BY APPLICATIONS IN
FINANCE AND BY RELEVANT CONNECTIONS WITH GEOMETRIC FLOWS; NAMELY, THE
SECOND ORDER EXTENSION WAS MOTIVATED BY ILLIQUIDITY MODELING, AND THE
CONTROLLED LOSS VERSION WAS INTRODUCED FOLLOWING THE PROBLEM OF QUANTILE
HEDGING. THE THIRD PART PRESENTS AN OVERVIEW OF BACKWARD STOCHASTIC
DIFFERENTIAL EQUATIONS AND THEIR EXTENSIONS TO THE QUADRATIC CASE.
BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS ARE INTIMATELY RELATED TO THE
STOCHASTIC VERSION OF PONTRYAGIN’S MAXIMUM PRINCIPLE AND CAN BE VIEWED
AS A STRONG VERSION OF STOCHASTIC TARGET PROBLEMS IN THE NON-MARKOV
CONTEXT. THE MAIN APPLICATIONS TO THE HEDGING PROBLEM UNDER MARKET
IMPERFECTIONS, THE OPTIMAL INVESTMENT PROBLEM IN THE EXPONENTIAL OR
POWER EXPECTED UTILITY FRAMEWORK, AND SOME RECENT DEVELOPMENTS IN THE
CONTEXT OF A NASH EQUILIBRIUM MODEL FOR INTERACTING INVESTORS, ARE
PRESENTED. THE BOOK CONCLUDES WITH A REVIEW OF THE NUMERICAL
APPROXIMATION TECHNIQUES FOR NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS
BASED ON MONOTONIC SCHEMES METHODS IN THE THEORY OF VISCOSITY SOLUTIONS
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
|
any_adam_object | 1 |
author | Touzi, Nizar |
author_GND | (DE-588)171244451 |
author_facet | Touzi, Nizar |
author_role | aut |
author_sort | Touzi, Nizar |
author_variant | n t nt |
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bvnumber | BV040591852 |
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classification_tum | MAT 000 MAT 606f MAT 496f |
collection | ZDB-2-SMA |
ctrlnum | (OCoLC)812053679 (DE-599)BVBBV040591852 |
discipline | Mathematik |
doi_str_mv | 10.1007/978-1-4614-4286-8 |
format | Electronic eBook |
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id | DE-604.BV040591852 |
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institution | BVB |
isbn | 1461442850 9781461442868 |
language | English |
oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-025419767 |
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spelling | Touzi, Nizar Verfasser (DE-588)171244451 aut Optimal stochastic control, stochastic target problems, and backward SDE Nizar Touzi. With chapter 13 by Agnès Tourin New York [u.a.] Springer 2013 1 Online-Ressource (X, 214 S.) txt rdacontent c rdamedia cr rdacarrier Fields Institute monographs 29 Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd rswk-swf Finanzmathematik (DE-588)4017195-4 gnd rswk-swf Stochastische optimale Kontrolle (DE-588)4207850-7 gnd rswk-swf Stochastische Differentialgleichung (DE-588)4057621-8 gnd rswk-swf Stochastische optimale Kontrolle (DE-588)4207850-7 s Finanzmathematik (DE-588)4017195-4 s Stochastische Differentialgleichung (DE-588)4057621-8 s Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 s DE-604 Erscheint auch als Druck-Ausgabe, Hardcover 978-1-4614-4285-1 Fields Institute monographs 29 (DE-604)BV044757996 29 https://doi.org/10.1007/978-1-4614-4286-8 Verlag Volltext Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025419767&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025419767&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Abstract |
spellingShingle | Touzi, Nizar Optimal stochastic control, stochastic target problems, and backward SDE Fields Institute monographs Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd Finanzmathematik (DE-588)4017195-4 gnd Stochastische optimale Kontrolle (DE-588)4207850-7 gnd Stochastische Differentialgleichung (DE-588)4057621-8 gnd |
subject_GND | (DE-588)4128900-6 (DE-588)4017195-4 (DE-588)4207850-7 (DE-588)4057621-8 |
title | Optimal stochastic control, stochastic target problems, and backward SDE |
title_auth | Optimal stochastic control, stochastic target problems, and backward SDE |
title_exact_search | Optimal stochastic control, stochastic target problems, and backward SDE |
title_full | Optimal stochastic control, stochastic target problems, and backward SDE Nizar Touzi. With chapter 13 by Agnès Tourin |
title_fullStr | Optimal stochastic control, stochastic target problems, and backward SDE Nizar Touzi. With chapter 13 by Agnès Tourin |
title_full_unstemmed | Optimal stochastic control, stochastic target problems, and backward SDE Nizar Touzi. With chapter 13 by Agnès Tourin |
title_short | Optimal stochastic control, stochastic target problems, and backward SDE |
title_sort | optimal stochastic control stochastic target problems and backward sde |
topic | Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd Finanzmathematik (DE-588)4017195-4 gnd Stochastische optimale Kontrolle (DE-588)4207850-7 gnd Stochastische Differentialgleichung (DE-588)4057621-8 gnd |
topic_facet | Nichtlineare partielle Differentialgleichung Finanzmathematik Stochastische optimale Kontrolle Stochastische Differentialgleichung |
url | https://doi.org/10.1007/978-1-4614-4286-8 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025419767&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025419767&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
volume_link | (DE-604)BV044757996 |
work_keys_str_mv | AT touzinizar optimalstochasticcontrolstochastictargetproblemsandbackwardsde |