Dynamic portfolio strategies: quantitative methods and empirical rules for incomplete information
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| Main Author: | |
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| Format: | Book |
| Language: | English |
| Published: |
Boston ; Dordrecht ; London
Kluwer Acad. Publ.
2002
|
| Series: | International series in operations research & management science
47 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XXVI, 199 S. graph. Darst. |
| ISBN: | 079237648X |
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| 245 | 1 | 0 | |a Dynamic portfolio strategies |b quantitative methods and empirical rules for incomplete information |c Nikolai Dokuchaev |
| 264 | 1 | |a Boston ; Dordrecht ; London |b Kluwer Acad. Publ. |c 2002 | |
| 300 | |a XXVI, 199 S. |b graph. Darst. | ||
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| 490 | 1 | |a International series in operations research & management science |v 47 | |
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Record in the Search Index
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|---|---|
| adam_text | ! Contents
List of Figures xi
List of Tables xiii
Acknowledgments xv
Introduction xvii
Part I Background
1. STOCHASTIC MARKET MODEL 3
1.1 Brief introduction to stochastic market models 3
1.2 Options market 6
1.3 Continuous-time multistock stochastic market model 9
Part II Model-free empirical strategies and their evaluation
2. TWO EMPIRICAL MODEL-FREE WINNING
STRATEGIES AND THEIR STATISTICAL
EVALUATION 15
2.1 A generic discrete-time market model 15
2.2 A bounded risk strategy 17
2.2.1 The strategy 17
2.2.2 Estimates of transaction costs 19
2.2.3 Average performance under probability assumptions 20
2.2.4 Experiments with historical data 22
2.3 A strategy with a risky numeraire 23
2.3.1 The strategy 24
2.3.2 Average performance on a probability space 25
vi DYNAMIC PORTFOLIO STRATEGIES
2.3.3 Experiments 26
2.4 Proofs 28
3. STRATEGIES FOR INVESTMENT IN OPTIONS 33
3.1 Introduction and definitions 33
3.2 The winning strategy 35
3.3 Numerical examples 36
3.4 A consequence for the seller and a paradox 38
3.5 Proofs 40
4. CONTINUOUS-TIME ANALOGS OF WINNING
STRATEGIES AND ASYMPTOTIC ARBITRAGE 43
4.1 Introduction 43
4.2 Definitions 44
4.3 Unbounded horizon: piecewise constant strategies 46
4.4 Continuous-time strategies for a single stock market with a
finite horizon 48
4.5 Strategies for a multi-stock market 49
4.6 Definitions for asymptotic arbitrage 50
4.7 Asymptotic arbitrage for the strategy (4.21) 53
4.8 Proofs 54
Part III Optimal strategies for the diffusion market model with observable
parameters
5. OPTIMAL STRATEGIES WITH DIRECT OBSERVATION
OF PARAMETERS 63
5.1 The market model 63
5.2 Solution via dynamic programming 65
5.3 Solution via optimal claim 66
5.3.1 Some additional assumptions 67
5.3.2 Special cases 67
5.3.3 Replicating special claims 68
5.3.4 Calculating the optimal strategy 69
5.3.5 The case of myopic strategies 70
5.4 Proofs 71
6. OPTIMAL PORTFOLIO COMPRESSION 77
6.1 Problem statement and definitions 77
I
I
j Contents vii
6.2 Optimal strategy for portfolio compression 80
6.3 A bond market: compression of the bond portfolio 82
6.4 Proofs 84
7. MAXEVHN CRITERION FOR OBSERVABLE BUT
NONPREDICTABLE PARAMETERS 89
7.1 Definitions and problem statement 89
7.2 Optimal solution of the maximin problem 95
7.3 Proofs 96
7.3.1 A duality theorem 98
7.3.2 Proof of Theorem 7.1 101
Part IV Optimal strategies based on historical data for markets with
nonobservable parameters
8. STRATEGIES BASED ON HISTORICAL PRICES
AND VOLUME: EXISTENCE RESULT 105
8.1 The model 105
8.2 A general problem and special cases 109
8.2.1 The general problem with constraints 109
8.2.2 Special cases of constraints and costs functions 109
8.3 Solution via dynamic programming 111
8.4 Additional definitions 115
8.5 Existence result for the general case 116
8.5.1 Auxiliary problem and additional assumptions 116
8.5.2 Existence result 117
8.6 The optimal strategy as a conditional expectation 118
8.7 Proofs 119
9. SOLUTION FOR LOG AND POWER UTILITIES WITH
HISTORICAL PRICES AND VOLUME 125
9.1 Replicating special polynomial claims 125
9.2 Log utility and minimum variance estimation of a 127
9.3 Power utility 127
9.4 Filters (estimators) for the appreciation rate 128
9.5 Portfolio compression for log utility 130
9.6 Some experiments with historical data 130
9.7 Proofs 135
I
I
viii DYNAMIC PORTFOLIO STRATEGIES
10. SOLUTION FOR GENERAL UTILITIES AND
CONSTRAINTS VIA PARABOLIC EQUATIONS 141
10.1 The model 141
10.2 Problem statement 142
10.3 Additional assumptions 143
10.4 A boundary problem for parabolic equations 144
10.5 The optimal strategy 145
10.6 Proofs 146
11. SPECIAL CASES AND EXAMPLES: REPLICATING WITH
GAP AND GOAL ACHIEVING 149
11.1 Additional assumptions and problem statement 149
11.2 Explicit formulas for optimal claims for special cases 151
11.2.1 Goal-achieving problem 151
11.2.2 Mean-variance criteria 153
11.2.3 Nonlinear concave utility functions 153
11.2.4 Nonconnected J(y) 154
11.3 Numerical examples 156
11.3.1 Solution of the goal-achieving problem 156
11.3.2 Optimal replication of a put option with a possible gap 157
11.3.3 Solution with logical constraints 158
11.4 Proofs 160
12. UNKNOWN DISTRIBUTION: MAXIMEN CRITERION
AND DUALITY APPROACH 165
12.1 Definitions and problem statement 165
12.2 A duality theorem 169
12.3 Duality approach to the maximin problem 170
12.4 Minimizing with respect to a(-) 171
12.5 An illustrative example 172
12.6 Proofs 174
13. ON REPLICATION OF CLAIMS 179
13.1 Replication of claims using option combinations 179
13.2 Superreplication under uncertainty and transaction costs 183
13.2.1 Market model and problem setting 184
13.2.2 Superreplicating strategy 188
13.3 Proofs 190
Contents a
References !95
Index
201
i
i
I
|
| adam_txt |
! Contents
List of Figures xi
List of Tables xiii
Acknowledgments xv
Introduction xvii
Part I Background
1. STOCHASTIC MARKET MODEL 3
1.1 Brief introduction to stochastic market models 3
1.2 Options market 6
1.3 Continuous-time multistock stochastic market model 9
Part II Model-free empirical strategies and their evaluation
2. TWO EMPIRICAL MODEL-FREE "WINNING"
STRATEGIES AND THEIR STATISTICAL
EVALUATION 15
2.1 A generic discrete-time market model 15
2.2 A bounded risk strategy 17
2.2.1 The strategy 17
2.2.2 Estimates of transaction costs 19
2.2.3 Average performance under probability assumptions 20
2.2.4 Experiments with historical data 22
2.3 A strategy with a risky numeraire 23
2.3.1 The strategy 24
2.3.2 Average performance on a probability space 25
vi DYNAMIC PORTFOLIO STRATEGIES
2.3.3 Experiments 26
2.4 Proofs 28
3. STRATEGIES FOR INVESTMENT IN OPTIONS 33
3.1 Introduction and definitions 33
3.2 The winning strategy 35
3.3 Numerical examples 36
3.4 A consequence for the seller and a paradox 38
3.5 Proofs 40
4. CONTINUOUS-TIME ANALOGS OF "WINNING"
STRATEGIES AND ASYMPTOTIC ARBITRAGE 43
4.1 Introduction 43
4.2 Definitions 44
4.3 Unbounded horizon: piecewise constant strategies 46
4.4 Continuous-time strategies for a single stock market with a
finite horizon 48
4.5 Strategies for a multi-stock market 49
4.6 Definitions for asymptotic arbitrage 50
4.7 Asymptotic arbitrage for the strategy (4.21) 53
4.8 Proofs 54
Part III Optimal strategies for the diffusion market model with observable
parameters
5. OPTIMAL STRATEGIES WITH DIRECT OBSERVATION
OF PARAMETERS 63
5.1 The market model 63
5.2 Solution via dynamic programming 65
5.3 Solution via optimal claim 66
5.3.1 Some additional assumptions 67
5.3.2 Special cases 67
5.3.3 Replicating special claims 68
5.3.4 Calculating the optimal strategy 69
5.3.5 The case of myopic strategies 70
5.4 Proofs 71
6. OPTIMAL PORTFOLIO COMPRESSION 77
6.1 Problem statement and definitions 77
I
I
j Contents vii
6.2 Optimal strategy for portfolio compression 80
6.3 A bond market: compression of the bond portfolio 82
6.4 Proofs 84
7. MAXEVHN CRITERION FOR OBSERVABLE BUT
NONPREDICTABLE PARAMETERS 89
7.1 Definitions and problem statement 89
7.2 Optimal solution of the maximin problem 95
7.3 Proofs 96
7.3.1 A duality theorem 98
7.3.2 Proof of Theorem 7.1 101
Part IV Optimal strategies based on historical data for markets with
nonobservable parameters
8. STRATEGIES BASED ON HISTORICAL PRICES
AND VOLUME: EXISTENCE RESULT 105
8.1 The model 105
8.2 A general problem and special cases 109
8.2.1 The general problem with constraints 109
8.2.2 Special cases of constraints and costs functions 109
8.3 Solution via dynamic programming 111
8.4 Additional definitions 115
8.5 Existence result for the general case 116
8.5.1 Auxiliary problem and additional assumptions 116
8.5.2 Existence result 117
8.6 The optimal strategy as a conditional expectation 118
8.7 Proofs 119
9. SOLUTION FOR LOG AND POWER UTILITIES WITH
HISTORICAL PRICES AND VOLUME 125
9.1 Replicating special polynomial claims 125
9.2 Log utility and minimum variance estimation of a 127
9.3 Power utility 127
9.4 Filters (estimators) for the appreciation rate 128
9.5 Portfolio compression for log utility 130
9.6 Some experiments with historical data 130
9.7 Proofs 135
I
I
viii DYNAMIC PORTFOLIO STRATEGIES
10. SOLUTION FOR GENERAL UTILITIES AND
CONSTRAINTS VIA PARABOLIC EQUATIONS 141
10.1 The model 141
10.2 Problem statement 142
10.3 Additional assumptions 143
10.4 A boundary problem for parabolic equations 144
10.5 The optimal strategy 145
10.6 Proofs 146
11. SPECIAL CASES AND EXAMPLES: REPLICATING WITH
GAP AND GOAL ACHIEVING 149
11.1 Additional assumptions and problem statement 149
11.2 Explicit formulas for optimal claims for special cases 151
11.2.1 Goal-achieving problem 151
11.2.2 Mean-variance criteria 153
11.2.3 Nonlinear concave utility functions 153
11.2.4 Nonconnected J(y) 154
11.3 Numerical examples 156
11.3.1 Solution of the goal-achieving problem 156
11.3.2 Optimal replication of a put option with a possible gap 157
11.3.3 Solution with logical constraints 158
11.4 Proofs 160
12. UNKNOWN DISTRIBUTION: MAXIMEN CRITERION
AND DUALITY APPROACH 165
12.1 Definitions and problem statement 165
12.2 A duality theorem 169
12.3 Duality approach to the maximin problem 170
12.4 Minimizing with respect to a(-) 171
12.5 An illustrative example 172
12.6 Proofs 174
13. ON REPLICATION OF CLAIMS 179
13.1 Replication of claims using option combinations 179
13.2 Superreplication under uncertainty and transaction costs 183
13.2.1 Market model and problem setting 184
13.2.2 Superreplicating strategy 188
13.3 Proofs 190
Contents a
References !95
Index
201
i
i
I |
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| id | DE-604.BV023568473 |
| illustrated | Illustrated |
| index_date | 2024-07-02T22:39:15Z |
| indexdate | 2024-07-09T21:24:41Z |
| institution | BVB |
| isbn | 079237648X |
| language | English |
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| spelling | Dokučaev, Nikolaj G. Verfasser (DE-588)124293263 aut Dynamic portfolio strategies quantitative methods and empirical rules for incomplete information Nikolai Dokuchaev Boston ; Dordrecht ; London Kluwer Acad. Publ. 2002 XXVI, 199 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier International series in operations research & management science 47 Kluwer's international series Portfolio management Investment analysis International series in operations research & management science 47 (DE-604)BV011630976 47 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016884429&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Dokučaev, Nikolaj G. Dynamic portfolio strategies quantitative methods and empirical rules for incomplete information International series in operations research & management science Portfolio management Investment analysis |
| title | Dynamic portfolio strategies quantitative methods and empirical rules for incomplete information |
| title_auth | Dynamic portfolio strategies quantitative methods and empirical rules for incomplete information |
| title_exact_search | Dynamic portfolio strategies quantitative methods and empirical rules for incomplete information |
| title_exact_search_txtP | Dynamic portfolio strategies quantitative methods and empirical rules for incomplete information |
| title_full | Dynamic portfolio strategies quantitative methods and empirical rules for incomplete information Nikolai Dokuchaev |
| title_fullStr | Dynamic portfolio strategies quantitative methods and empirical rules for incomplete information Nikolai Dokuchaev |
| title_full_unstemmed | Dynamic portfolio strategies quantitative methods and empirical rules for incomplete information Nikolai Dokuchaev |
| title_short | Dynamic portfolio strategies |
| title_sort | dynamic portfolio strategies quantitative methods and empirical rules for incomplete information |
| title_sub | quantitative methods and empirical rules for incomplete information |
| topic | Portfolio management Investment analysis |
| topic_facet | Portfolio management Investment analysis |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016884429&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV011630976 |
| work_keys_str_mv | AT dokucaevnikolajg dynamicportfoliostrategiesquantitativemethodsandempiricalrulesforincompleteinformation |