Holdings: Optimal stochastic control, stochastic target problems, and backward SDE

Optimal stochastic control, stochastic target problems, and backward SDE:

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Bibliographic Details
Main Author:	Touzi, Nizar (Author)
Format:	Electronic eBook
Language:	English
Published:	New York [u.a.] Springer 2013
Series:	Fields Institute monographs 29
Subjects:	Nichtlineare partielle Differentialgleichung Finanzmathematik Stochastische optimale Kontrolle Stochastische Differentialgleichung
Online Access:	BTU01 TUM01 UBA01 UBM01 UBT01 UBW01 UPA01 Volltext Inhaltsverzeichnis Abstract
Physical Description:	1 Online-Ressource (X, 214 S.)
ISBN:	1461442850 9781461442868
DOI:	10.1007/978-1-4614-4286-8

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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.
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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

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