Markets with transaction costs: mathematical theory
Gespeichert in:
| Beteiligte Personen: | , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2009
|
| Schriftenreihe: | Springer Finance
|
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016607532&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke |
| Umfang: | XIV, 294 S. graph. Darst. |
| ISBN: | 9783540681205 9783642262784 |
Internformat
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| 245 | 1 | 0 | |a Markets with transaction costs |b mathematical theory |c Yuri Kabanov ; Mher Safarian |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2009 | |
| 300 | |a XIV, 294 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| 490 | 0 | |a Springer Finance | |
| 500 | |a Hier auch später erschienene, unveränderte Nachdrucke | ||
| 650 | 0 | 7 | |a Arbitrage-Pricing-Theorie |0 (DE-588)4112584-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Hedging |0 (DE-588)4123357-8 |2 gnd |9 rswk-swf |
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| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-016607532 | |
Datensatz im Suchindex
| DE-BY-TUM_call_number | 0102 MAT 605f 2010 A 2489 |
|---|---|
| DE-BY-TUM_katkey | 1704343 |
| DE-BY-TUM_location | 01 |
| DE-BY-TUM_media_number | 040010227648 |
| _version_ | 1821933735367409664 |
| adam_text | Contents
Approximative
Hedging
................................... 1
1.1 Black-Scholes
Formula Revisited
.......................... 1
1.1.1
Pricing by Replication
............................. 1
1.1.2
Explicit Formulae
................................. 3
1.1.3
Discussion
........................................ 5
1.2
Leland-Lott Theorem
.................................... 7
1.2.1
Formulation and Comments
........................ 7
1.2.2
Proof
............................................ 9
1.3
Constant Coefficient: Discrepancy
......................... 17
1.3.1
Main Result
...................................... 17
1.3.2
Discussion
........................................ 19
1.3.3
Pergamenshchikov Theorem
........................ 20
1.4
Rate of Convergence of the Replication Error
............... 21
1.4.1
Formulation
...................................... 21
1.4.2
Preparatory Manipulations
......................... 23
1.4.3
Convenient Representations, Explicit Formulae, and
Useful Bounds
.................................... 26
1.4.4
Tools
............................................ 34
1.4.5
Analysis of the Principal Terms: Proof
of Proposition
1.4.5................................ 35
1.4.6
Analysis of the Residual Rln
........................ 36
1.4.7
Analysis of the Residual R2n
........................ 39
1.4.8
Asymptotics of Gaussian Integrals
................... 49
1.5
Functional Limit Theorem for a
= 1/2..................... 51
1.5.1
Formulation
...................................... 51
1.5.2
Limit Theorem for
Semimartingale
Scheme
........... 52
1.5.3
Problem Reformulation
............................ 53
1.5.4
Tightness
........................................ 55
1.5.5
Limit Measure
.................................... 57
1.5.6
Identification of the Limit
.......................... 58
Contents
1.6 Superhedging
by Buy-and-Hokł
........................... 59
1.6.1 Levental-Skorokhod
Theorem
....................... 59
1.6.2
Proof
............................................ 61
1.6.3
Extensions for One-Side Transaction Costs
........... 64
1.6.4
Hedging of Vector-Valued Contingent Claims
......... 68
Arbitrage Theory for Prictionless Markets
................. 71
2.1
Models without Friction
.................................. 71
2.1.1
DMW Theorem
................................... 71
2.1.2
Auxiliary Results: Measurable Subsequences and
the Kreps-Yan Theorem
........................... 74
2.1.3
Proof of the DMW Theorem
........................ 75
2.1.4
Fast Proof of the DMW Theorem
................... 77
2.1.5
NA and Conditional Distributions of Price Increments
. 78
2.1.6
Comment on Absolute Continuous Martingale Measures
80
2.1.7
Complete Markets and Replicable Contingent Claims
.. 80
2.1.8
DMW Theorem with Restricted Information
.......... 81
2.1.9
Hedging Theorem for European-Type Options
........ 82
2.1.10
Stochastic Discounting Factors
...................... 85
2.1.11
Hedging Theorem for American-Type Options
........ 85
2.1.12
Optional Decomposition Theorem
................... 86
2.1.13
Martingale Measures with Bounded Densities
......... 87
2.1.14
Utility Maximization and Convex Duality
............ 90
2.2
Discrete-Time Infinite-Horizon Model
...................... 93
2.2.1
Martingale Measures in Infinite-Horizon Model
........ 93
2.2.2
No Free Lunch for Models with Infinite Time Horizon
.. 95
2.2.3
No Free Lunch with Vanishing Risk
.................. 99
2.2.4
Example: Retiring Process
........................ 101
2.2.5
The Delbaen-Schachemayer Theory in Continuous
Time
............................................ 103
Arbitrage Theory under Transaction Costs
................105
3.1
Models with Transaction Costs
............................105
3.1.1
Basic Model
......................................105
3.1.2
Variants
..........................................110
3.1.3
No-arbitrage problem: NAW for finite
Ω
..............114
3.1.4
No-arbitrage Problem: NA3 for Finite
Ω
..............115
3.2
No-arbitrage Problem: Abstract Approach
..................117
3.2.1
NAr- and 7V.4S-Properties: Formulations
..............117
3.2.2
NAr- and
M4s-Properties:
Proofs
....................120
3.2.3
The Grigoriev Theorem
............................124
3.2.4
Counterexamples
..................................128
3.2.5
A Complement: The
Rásonyi
Theorem
...............131
3.2.6
Arbitrage Opportunities of the Second Kind
..........134
3.3
Hedging of European Options
.............................137
Contents xiii
3.3.1
Hedging
Theorem:
Finite
Ω
.........................137
3.3.2
Hedging Theorem: Discrete Time, Arbitrary
Ω
........138
3.4
Hedging of American Options
.............................139
3.4.1
American Options: Finite
Ω
........................139
3.4.2
American Options: Arbitrary
Ω
.....................141
3.4.3
Complementary Results and Comments
..............143
3.5
Ramifications
...........................................144
3.5.1
Models with Incomplete Information
.................144
3.5.2
No Arbitrage Criteria: Finite
Ω
.....................147
3.5.3
No Arbitrage Criteria: Arbitrary
Ω
..................150
3.5.4
Hedging Theorem
.................................154
3.6
Hedging Theorems: Continuous Time
......................155
3.6.1
Introductory Comments
............................155
3.6.2
Model Specification
................................156
3.6.3
Hedging Theorem in Abstract Setting
................158
3.6.4
Hedging Theorem: Proof
...........................160
3.6.5
Rásonyi
Counterexample
...........................162
3.6.6
Campi-Sehachermayer Model
.......................164
3.6.7
Hedging Theorem for American Options
..............170
3.6.8
When Does a Consistent Price System Exist?
.........174
3.7
Asymptotic Arbitrage Opportunities of the Second Kind
.....176
Consumption—Investment Problems
........................183
4.1
Consumption-Investment without Friction
..................183
4.1.1
The Merton Problem
..............................183
4.1.2
The HJB Equation and a Verification Theorem
........186
4.1.3
Proof of the Merton Theorem
.......................187
4.1.4
Discussion
........................................188
4.1.5
Robustness of the Merton Solution
..................190
4.2
Consumption-Investment under Transaction Costs
...........190
4.2.1
The Model
.......................................190
4.2.2
Goal Functional
..................................193
4.2.3
The Hamilton-Jacobi-Bellman Equation
.............194
4.2.4
Viscosity Solutions
................................194
4.2.5
Ishii s Lemma
.....................................199
4.3
Uniqueness of the Solution and Lyapunov Functions
.........200
4.3.1
Uniqueness Theorem
...............................200
4.3.2
Existence of Lyapunov Functions and Classical
Supersolutions
....................................202
4.4
Supersolutions
and Properties of the Bellman Function
.......204
4.4.1
When is
W
Finite on Kl
...........................204
4.4.2
Strict Local
Supersolutions
.........................206
4.5
Dynamic Programming Principle
..........................208
4.6
The Bellman Function and the HJB Equation
...............212
4.7
Properties of the Bellman Function
........................213
xiv Contents
4.7.1
The Subdifferential: Generalities
....................213
4.7.2
The Bellman Function of the Two-Asset Model
.......215
4.7.3
Lower Bounds for the Bellman Function
..............216
4.8
The Davis-Norman Solution
..............................217
4.8.1
Two-Asset Model: The Result
.......................217
4.8.2
Structure of Bellman Function
......................219
4.8.3
Study of the Scalar Problem
........................222
4.8.4
Skorohod Problem
.................................228
4.8.5
Optimal Strategy
..................................229
4.8.6
Precisions on the No-Transaction Region
.............232
4.9
Liquidity Premium
......................................234
4.9.1
Non-Robustness with Respect to Transaction Costs
.... 234
4.9.2
First-Order Asymptotic Expansion
..................240
4.9.3
Exceptional Case:
0 = 1............................245
5
Appendix
..................................................247
5.1
Facts from Convex Analysis
...............................247
5.2
Césaro
Convergence
.....................................250
5.2.1
Komlós
Theorem
..................................250
5.2.2
Application to Convex Minimization in L1
............250
5.2.3 Von Weizsäcker
Theorem
...........................250
5.2.4
Application to Convex Minimization in L°
............253
5.2.5
Delbaen-Schachermayer Lemma
.....................253
5.3
Facts from Probability
...................................254
5.3.1
Essential Supremum
...............................254
5.3.2
Generalized Martingales
............................255
5.3.3
Equivalent Probabilities
............................256
5.3.4
Snell Envelopes of Q-Martingales
....................257
5.4
Measurable Selection
.....................................258
5.5
Fatou-Convergence and Bipolar Theorem in L°
..............261
5.6
Skorokhod Problem and SDE with Reflections
..............262
5.6.1
Deterministic Skorokhod Problem
...................263
5.6.2
Skorokhod Mapping
...............................264
5.6.3
Stochastic Skorokhod Problem
......................265
Bibliographical Comments
.....................................267
References
.....................................................279
Index
........................................................293
|
| any_adam_object | 1 |
| author | Kabanov, Jurij M. 1948- Safarian, Mher M. 1972- |
| author_GND | (DE-588)124079199 (DE-588)11537227X |
| author_facet | Kabanov, Jurij M. 1948- Safarian, Mher M. 1972- |
| author_role | aut aut |
| author_sort | Kabanov, Jurij M. 1948- |
| author_variant | j m k jm jmk m m s mm mms |
| building | Verbundindex |
| bvnumber | BV023425161 |
| classification_rvk | QP 890 SK 980 |
| classification_tum | MAT 605f WIR 170f |
| ctrlnum | (OCoLC)614459625 (DE-599)DNB989061361 |
| dewey-full | 332.645 |
| dewey-hundreds | 300 - Social sciences |
| dewey-ones | 332 - Financial economics |
| dewey-raw | 332.645 |
| dewey-search | 332.645 |
| dewey-sort | 3332.645 |
| dewey-tens | 330 - Economics |
| discipline | Mathematik Wirtschaftswissenschaften |
| format | Book |
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| id | DE-604.BV023425161 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T13:16:04Z |
| institution | BVB |
| isbn | 9783540681205 9783642262784 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016607532 |
| oclc_num | 614459625 |
| open_access_boolean | |
| owner | DE-N2 DE-355 DE-BY-UBR DE-521 DE-91G DE-BY-TUM DE-12 DE-188 DE-83 DE-11 DE-20 DE-19 DE-BY-UBM |
| owner_facet | DE-N2 DE-355 DE-BY-UBR DE-521 DE-91G DE-BY-TUM DE-12 DE-188 DE-83 DE-11 DE-20 DE-19 DE-BY-UBM |
| physical | XIV, 294 S. graph. Darst. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Springer |
| record_format | marc |
| series2 | Springer Finance |
| spellingShingle | Kabanov, Jurij M. 1948- Safarian, Mher M. 1972- Markets with transaction costs mathematical theory Arbitrage-Pricing-Theorie (DE-588)4112584-8 gnd Hedging (DE-588)4123357-8 gnd Transaktionskosten (DE-588)4060619-3 gnd Mathematisches Modell (DE-588)4114528-8 gnd Unvollkommener Kreditmarkt (DE-588)4128333-8 gnd |
| subject_GND | (DE-588)4112584-8 (DE-588)4123357-8 (DE-588)4060619-3 (DE-588)4114528-8 (DE-588)4128333-8 |
| title | Markets with transaction costs mathematical theory |
| title_auth | Markets with transaction costs mathematical theory |
| title_exact_search | Markets with transaction costs mathematical theory |
| title_full | Markets with transaction costs mathematical theory Yuri Kabanov ; Mher Safarian |
| title_fullStr | Markets with transaction costs mathematical theory Yuri Kabanov ; Mher Safarian |
| title_full_unstemmed | Markets with transaction costs mathematical theory Yuri Kabanov ; Mher Safarian |
| title_short | Markets with transaction costs |
| title_sort | markets with transaction costs mathematical theory |
| title_sub | mathematical theory |
| topic | Arbitrage-Pricing-Theorie (DE-588)4112584-8 gnd Hedging (DE-588)4123357-8 gnd Transaktionskosten (DE-588)4060619-3 gnd Mathematisches Modell (DE-588)4114528-8 gnd Unvollkommener Kreditmarkt (DE-588)4128333-8 gnd |
| topic_facet | Arbitrage-Pricing-Theorie Hedging Transaktionskosten Mathematisches Modell Unvollkommener Kreditmarkt |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016607532&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT kabanovjurijm marketswithtransactioncostsmathematicaltheory AT safarianmherm marketswithtransactioncostsmathematicaltheory |
Inhaltsverzeichnis
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Paper/Kapitel scannen lassen
Teilbibliothek Mathematik & Informatik
| Signatur: |
0102 MAT 605f 2010 A 2489 Lageplan |
|---|---|
| Exemplar 1 | Ausleihbar Am Standort |