Continuous-time stochastic control and optimization with financial applications:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Dordrecht [u.a.]
Springer
[2009]
|
| Series: | Stochastic modelling and applied probability
61 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 223 - 229 |
| Physical Description: | XVII, 232 Seiten |
| ISBN: | 9783540894995 |
Staff View
MARC
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Record in the Search Index
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| adam_text | CONTENTS SOME ELEMENTS OF STOCHASTIC ANALYSIS 1 1.1 STOCHASTIC PROCESSES
1 1.1.1 FILTRATION AND PROCESSES 1 1.1.2 STOPPING TIMES 3 1.1.3 BROWNIAN
MOTION 5 1.1.4 MARTINGALES, SEMIMARTINGALES 6 1.2 STOCHASTIC INTEGRAL
AND APPLICATIONS 12 1.2.1 STOCHASTIC INTEGRAL WITH RESPECT TO A
CONTINUOUS SEMIMARTINGALE .. 12 1.2.2 ITOE PROCESS 16 1.2.3 ITOE S FORMULA
17 1.2.4 MARTINGALE REPRESENTATION THEOREM 18 1.2.5 GIRSANOV S THEOREM
18 1.3 STOCHASTIC DIFFERENTIAL EQUATIONS 22 1.3.1 STRONG SOLUTIONS OF
SDE 22 1.3.2 ESTIMATES ON THE MOMENTS OF SOLUTIONS TO SDE 24 1.3.3
FEYNMAN-KAC FORMULA 25 STOCHASTIC OPTIMIZATION PROBLEMS. EXAMPLES IN
FLNANCE 27 2.1 INTRODUCTION 27 2.2 EXAMPLES 28 2.2.1 PORTFOLIO
ALLOCATION 28 2.2.2 PRODUCTION-CONSUMPTION MODEL 29 2.2.3 IRREVERSIBLE
INVESTMENT MODEL 30 2.2.4 QUADRATIC HEDGING OF OPTIONS 31 2.2.5
SUPERREPLICATION COST IN UNCERTAIN VOLATILITY 31 2.2.6 OPTIMAL SELLING
OF AN ASSET 32 2.2.7 VALUATION OF NATURAL RESOURCES 32 2.3 OTHER
OPTIMIZATION PROBLEMS IN FINANCE 32 2.3.1 ERGODIC AND RISK-SENSITIVE
CONTROL PROBLEMS 32 2.3.2 SUPERREPLICATION UNDER GAMMA CONSTRAINTS 33
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/992498597 DIGITALISIERT
DURCH XII CONTENTS 2.3.3 ROBUST UTILITY MAXIMIZATION PROBLEM AND RISK
MEASURES 33 2.3.4 FORWARD PERFORMANCE CRITERION 34 2.4 BIBLIOGRAPHICAL
REMARKS 34 3 THE CLASSICAL PDE APPROACH TO DYNAMIC PROGRAMMING 37 3.1
INTRODUCTION 37 3.2 CONTROLLED DIFFUSION PROCESSES 37 3.3 DYNAMIC
PROGRAMMING PRINCIPLE 40 3.4 HAMILTON-JACOBI-BELLMAN EQUATION 42 3.4.1
FORMAL DERIVATION OF HJB 42 3.4.2 REMARKS AND EXTENSIONS 45 3.5
VERIFICATION THEOREM 47 3.6 APPLICATIONS 51 3.6.1 MERTON PORTFOLIO
ALLOCATION PROBLEM IN FINITE HORIZON 51 3.6.2 INVESTMENT-CONSUMPTION
PROBLEM WITH RANDOM TIME HORIZON 53 3.6.3 A MODEL OF
PRODUCTION-CONSUMPTION ON INFINITE HORIZON 55 3.7 EXAMPLE OF SINGULAR
STOCHASTIC CONTROL PROBLEM 58 3.8 BIBLIOGRAPHICAL REMARKS 59 4 THE
VISCOSITY SOLUTIONS APPROACH TO STOCHASTIC CONTROL PROBLEMS 61 4.1
INTRODUCTION 61 4.2 DEFINITION OF VISCOSITY SOLUTIONS 61 4.3 FROM
DYNAMIC PROGRAMMING TO VISCOSITY SOLUTIONS OF HJB EQUATIONS .... 64
4.3.1 VISCOSITY PROPERTIES INSIDE THE DOMAIN 64 4.3.2 TERMINAL CONDITION
69 4.4 COMPARISON PRINCIPLES AND UNIQUENESS RESULTS 75 4.4.1 CLASSICAL
COMPARISON PRINCIPLE 76 4.4.2 STRONG COMPARISON PRINCIPLE 77 4.5 AN
IRREVERSIBLE INVESTMENT MODEL 82 4.5.1 PROBLEM 82 4.5.2 REGULARITY AND
CONSTRUCTION OF THE VALUE FUNCTION 83 4.5.3 OPTIMAL STRATEGY 88 4.6
SUPERREPLICATION COST IN UNCERTAIN VOLATILITY MODEL 89 4.6. CONTENTS
XIII 5.3 OPTIMAL SWITCHING 107 5.3.1 PROBLEM FORMULATION 108 5.3.2
DYNAMIC PROGRAMMING AND SYSTEM OF VARIATIONAL INEQUALITIES .... 109
5.3.3 SWITCHING REGIONS 114 5.3.4 THE ONE-DIMENSIONAL CASE 116 5.3.5
EXPLICIT SOLUTION IN THE TWO-REGIME CASE 119 5.4 BIBLIOGRAPHICAL REMARKS
137 BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS AND OPTIMAL CONTROL 139
6.1 INTRODUCTION 139 6.2 GENERAL PROPERTIES 139 6.2.1 EXISTENCE AND
UNIQUENESS RESULTS 139 6.2.2 LINEAR BSDE 141 6.2.3 COMPARISON PRINCIPLES
142 6.3 BSDE, PDE AND NONLINEAR FEYNMAN-KAC FORMULAE 143 6.4 CONTROL AND
BSDE 147 6.4.1 OPTIMIZATION OF A FAMILY OF BSDES 147 6.4.2 STOCHASTIC
MAXIMUM PRINCIPLE 149 6.5 REFLECTED BSDES AND OPTIMAL STOPPING PROBLEMS
152 6.5.1 EXISTENCE AND APPROXIMATION VIA PENALIZATION 154 6.5.2
CONNECTION WITH VARIATIONAL INEQUALITIES 159 6.6 APPLICATIONS 162 6.6.1
EXPONENTIAL UTILITY MAXIMIZATION WITH OPTION PAYOFF 162 6.6.2
MEAN-VARIANCE CRITERION FOR PORTFOLIO SELECTION 165 6.7 BIBLIOGRAPHICAL
REMARKS 169 MARTINGALE AND CONVEX DUALITY METHODS 171 7.1 INTRODUCTION
171 7.2 DUAL REPRESENTATION FOR THE SUPERREPLICATION COST 172 7.2.1
FORMULATION OF THE SUPERREPLICATION PROBLEM 172 7.2.2 MARTINGALE
PROBABILITY MEASURES AND NO ARBITRAGE 173 7.2.3 OPTIONAL DECOMPOSITION
THEOREM AND DUAL REPRESENTATION FOR THE SUPERREPLICATION COST 174 7.2.
XIV CONTENTS 7.4.4 PROBLEM RESOLUTION BY CHANGE OF NUMERAIRE 206 7.4.5
EXAMPLE 210 7.5 BIBLIOGRAPHICAL REMARKS 212 A COMPLEMENTS OF INTEGRATION
213 A.L UNIFORM INTEGRABILITY 213 A.2 ESSENTIAL SUPREMUM OF A FAMILY OF
RANDOM VARIABLES 215 A.3 SOME COMPACTNESS THEOREMS IN PROBABILITY 215 B
CONVEX ANALYSIS CONSIDERATIONS 217 B.L SEMICONTINUOUS, CONVEX FUNCTIONS
217 B.2 FENCHEL-LEGENDRE TRANSFORM 218 B.3 EXAMPLE IN K 219 REFERENCES
223 INDEX 231
|
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| dewey-ones | 332 - Financial economics 519 - Probabilities and applied mathematics |
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| dewey-search | 332.015962 519.6/2 |
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| indexdate | 2024-07-09T21:40:06Z |
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| isbn | 9783540894995 |
| language | English |
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| series2 | Stochastic modelling and applied probability |
| spelling | Pham, Huyen 1968- Verfasser (DE-588)120714574 aut Continuous-time stochastic control and optimization with financial applications Huyên Pham Dordrecht [u.a.] Springer [2009] © 2009 XVII, 232 Seiten txt rdacontent n rdamedia nc rdacarrier Stochastic modelling and applied probability 61 Literaturverz. S. 223 - 229 Dynamische Optimierung stw Finanzmathematik - Stochastische Optimierung Finanzmathematik stw Kontrolltheorie stw Portfolio-Management stw Stochastischer Prozess stw Theorie stw Business mathematics Mathematical optimization Stochastic control theory Stochastische Optimierung (DE-588)4057625-5 gnd rswk-swf Finanzmathematik (DE-588)4017195-4 gnd rswk-swf Finanzmathematik (DE-588)4017195-4 s Stochastische Optimierung (DE-588)4057625-5 s DE-604 Erscheint auch als Online-Ausgabe 978-3-540-89500-8 Stochastic modelling and applied probability 61 (DE-604)BV019623501 61 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017601422&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Pham, Huyen 1968- Continuous-time stochastic control and optimization with financial applications Stochastic modelling and applied probability Dynamische Optimierung stw Finanzmathematik - Stochastische Optimierung Finanzmathematik stw Kontrolltheorie stw Portfolio-Management stw Stochastischer Prozess stw Theorie stw Business mathematics Mathematical optimization Stochastic control theory Stochastische Optimierung (DE-588)4057625-5 gnd Finanzmathematik (DE-588)4017195-4 gnd |
| subject_GND | (DE-588)4057625-5 (DE-588)4017195-4 |
| title | Continuous-time stochastic control and optimization with financial applications |
| title_auth | Continuous-time stochastic control and optimization with financial applications |
| title_exact_search | Continuous-time stochastic control and optimization with financial applications |
| title_full | Continuous-time stochastic control and optimization with financial applications Huyên Pham |
| title_fullStr | Continuous-time stochastic control and optimization with financial applications Huyên Pham |
| title_full_unstemmed | Continuous-time stochastic control and optimization with financial applications Huyên Pham |
| title_short | Continuous-time stochastic control and optimization with financial applications |
| title_sort | continuous time stochastic control and optimization with financial applications |
| topic | Dynamische Optimierung stw Finanzmathematik - Stochastische Optimierung Finanzmathematik stw Kontrolltheorie stw Portfolio-Management stw Stochastischer Prozess stw Theorie stw Business mathematics Mathematical optimization Stochastic control theory Stochastische Optimierung (DE-588)4057625-5 gnd Finanzmathematik (DE-588)4017195-4 gnd |
| topic_facet | Dynamische Optimierung Finanzmathematik - Stochastische Optimierung Finanzmathematik Kontrolltheorie Portfolio-Management Stochastischer Prozess Theorie Business mathematics Mathematical optimization Stochastic control theory Stochastische Optimierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017601422&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV019623501 |
| work_keys_str_mv | AT phamhuyen continuoustimestochasticcontrolandoptimizationwithfinancialapplications |