Numerical solution of stochastic differential equations with jumps in finance:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2010
|
| Schriftenreihe: | Stochastic modelling and applied probability
64 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XXVIII, 856 Seiten graph. Darst. |
| ISBN: | 9783642120572 |
Internformat
MARC
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| 040 | |a DE-604 |b ger |e rda | ||
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| 100 | 1 | |a Platen, Eckhard |d 1949- |e Verfasser |0 (DE-588)115479201 |4 aut | |
| 245 | 1 | 0 | |a Numerical solution of stochastic differential equations with jumps in finance |c Eckard Platen ; Nicola Bruti-Liberati |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2010 | |
| 300 | |a XXVIII, 856 Seiten |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Stochastic modelling and applied probability |v 64 | |
| 650 | 0 | 7 | |a Stochastische Differentialgleichung |0 (DE-588)4057621-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Finanzmathematik |0 (DE-588)4017195-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Zeitdiskrete Approximation |0 (DE-588)4401310-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Monte-Carlo-Simulation |0 (DE-588)4240945-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Poisson-Prozess |0 (DE-588)4174971-6 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Stochastische Differentialgleichung |0 (DE-588)4057621-8 |D s |
| 689 | 0 | 1 | |a Poisson-Prozess |0 (DE-588)4174971-6 |D s |
| 689 | 0 | 2 | |a Zeitdiskrete Approximation |0 (DE-588)4401310-3 |D s |
| 689 | 0 | 3 | |a Monte-Carlo-Simulation |0 (DE-588)4240945-7 |D s |
| 689 | 0 | 4 | |a Finanzmathematik |0 (DE-588)4017195-4 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Bruti-Liberati, Nicola |d 1975-2007 |e Verfasser |0 (DE-588)1311349863 |4 aut | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-3-642-13694-8 |
| 830 | 0 | |a Stochastic modelling and applied probability |v 64 |w (DE-604)BV019623501 |9 64 | |
| 856 | 4 | 2 | |m Digitalisierung UB Passau |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020500264&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-020500264 | ||
Datensatz im Suchindex
| _version_ | 1804143165602529280 |
|---|---|
| adam_text | Contents
Preface
......................................................
V
Suggestions
for the Reader
..................................
XV
Basic Notation
.............................................. XIX
Motivation and Brief Survey
.................................XXIII
1
Stochastic Differential Equations with Jumps
.............. 1
1.1
Stochastic Processes
..................................... 1
1.2
Supermartingales and Martingales
......................... 16
1.3
Quadratic Variation and Covariation
....................... 23
1.4
Ito
Integral
............................................. 26
1.5
Ito
Formula
............................................. 34
1.6
Stochastic Differential Equations
.......................... 38
1.7
Linear SDEs
............................................ 45
1.8
SDEs with Jumps
....................................... 53
1.9
Existence and Uniqueness of Solutions of SDEs
.............. 57
1.10
Exercises
............................................... 59
2
Exact Simulation of Solutions of SDEs
..................... 61
2.1
Motivation of Exact Simulation
........................... 61
2.2
Sampling from Transition Distributions
.................... 63
2.3
Exact Solutions of Multi-dimensional SDEs
................. 78
2.4
Functions of Exact Solutions
.............................. 99
2.5
Almost Exact Solutions by Conditioning
....................105
2.6
Almost Exact Simulation by Time Change
..................113
2.7
Functionals of Solutions of SDEs
..........................123
2.8
Exercises
...............................................136
X
Contents
3 Benchmark
Approach to Finance and Insurance
...........139
3.1
Market Model
...........................................139
3.2
Best Performing Portfolio
................................142
3.3
Supermartingale
Property and Pricing
.....................145
3.4
Diversification
..........................................149
3.5
Real World Pricing Under Some Models
....................158
3.6
Real World Pricing Under the
МММ
......................168
3.7
Binomial Option Pricing
.................................176
3.8
Exercises
...............................................185
4
Stochastic Expansions
.....................................187
4.1
Introduction to Wagner-Platen Expansions
.................187
4.2
Multiple Stochastic Integrals
..............................195
4.3
Coefficient Functions
.....................................202
4.4
Wagner-Platen Expansions
...............................206
4.5
Moments of Multiple Stochastic Integrals
...................211
4.6
Exercises
...............................................230
5
Introduction to Scenario Simulation
.......................233
5.1
Approximating Solutions of ODEs
.........................233
5.2
Scenario Simulation
......................................245
5.3
Strong Taylor Schemes
...................................252
5.4
Derivative-Free Strong Schemes
...........................266
5.5
Exercises
...............................................271
6
Regular Strong Taylor Approximations with Jumps
........273
6.1
Discrete-Time Approximation
.............................273
6.2
Strong Order
1.0
Taylor Scheme
...........................278
6.3
Commutativity Conditions
................................286
6.4
Convergence Results
.....................................289
6.5
Lemma on Multiple
Ito
Integrals
..........................292
6.6
Proof of the Convergence Theorem
........................302
6.7
Exercises
...............................................307
7
Regular Strong
Ito
Approximations
........................309
7.1
Explicit Regular Strong Schemes
..........................309
7.2
Drift-Implicit Schemes
...................................316
7.3
Balanced Implicit Methods
...............................321
7.4
Predictor-Corrector Schemes
..............................326
7.5
Convergence Results
.....................................331
7.6
Exercises
...............................................346
Contents
XI
8
Jump-Adapted Strong Approximations
....................347
8.1
Introduction to Jump-Adapted Approximations
.............347
8.2
Jump-Adapted Strong Taylor Schemes
.....................350
8.3
Jump-Adapted Derivative-Free Strong Schemes
..............355
8.4
Jump-Adapted Drift-Implicit Schemes
......................356
8.5
Predictor-Corrector Strong Schemes
.......................359
8.6
Jump-Adapted Exact Simulation
..........................361
8.7
Convergence Results
.....................................362
8.8
Numerical Results on Strong Schemes
......................368
8.9
Approximation of Pure Jump Processes
....................375
8.10
Exercises
...............................................388
9
Estimating Discretely Observed Diffusions
.................389
9.1
Maximum Likelihood Estimation
..........................389
9.2
Discretization of Estimators
..............................393
9.3
Transform Functions for Diffusions
........................397
9.4
Estimation of
Affine
Diffusions
............................404
9.5
Asymptotics of Estimating Functions
......................409
9.6
Estimating Jump Diffusions
...............................413
9.7
Exercises
...............................................417
10
Filtering
...................................................419
10.1
Kalman-Bucy Filter
.....................................419
10.2
Hidden Markov Chain Filters
.............................424
10.3
Filtering a Mean Reverting Process
........................433
10.4
Balanced Method in Filtering
.............................447
10.5
A Benchmark Approach to Filtering in Finance
.............456
10.6
Exercises
...............................................475
11
Monte Carlo Simulation of SDEs
..........................477
11.1
Introduction to Monte Carlo Simulation
....................477
11.2
Weak Taylor Schemes
....................................481
11.3
Derivative-Free Weak Approximations
......................491
11.4
Extrapolation Methods
...................................495
11.5
Implicit and Predictor-Corrector Methods
..................497
11.6
Exercises
...............................................504
12
Regular Weak Taylor Approximations
.....................507
12.1
Weak Taylor Schemes
....................................507
12.2
Commutativity Conditions
................................514
12.3
Convergence Results
.....................................517
12.4
Exercises
...............................................522
XII Contents
13
Jump-Adapted Weak Approximations
.....................523
13.1
Jump-Adapted Weak Schemes
............................523
13.2
Derivative-Free Schemes
..................................529
13.3
Predictor-Corrector Schemes
..............................530
13.4
Some Jump-Adapted Exact Weak Schemes
.................533
13.5
Convergence of Jump-Adapted Weak Taylor Schemes
........534
13.6
Convergence of Jump-Adapted Weak Schemes
...............543
13.7
Numerical Results on Weak Schemes
.......................548
13.8
Exercises
...............................................569
14
Numerical Stability
........................................571
14.1
Asymptotic p-Stability
...................................571
14.2
Stability of Predictor-Corrector Methods
...................576
14.3
Stability of Some Implicit Methods
........................583
14.4
Stability of Simplified Schemes
............................586
14.5
Exercises
...............................................590
15
Martingale Representations and Hedge Ratios
.............591
15.1
General Contingent Claim Pricing
.........................591
15.2
Hedge Ratios for One-dimensional Processes
................595
15.3
Explicit Hedge Ratios
....................................601
15.4
Martingale Representation for Non-Smooth Payoffs
..........606
15.5
Absolutely Continuous Payoff Functions
....................616
15.6
Maximum of Several Assets
...............................621
15.7
Hedge Ratios for
Lookback
Options
........................627
15.8
Exercises
...............................................635
16
Variance Reduction Techniques
............................637
16.1
Various Variance Reduction Methods
......................637
16.2
Measure Transformation Techniques
.......................645
16.3
Discrete-Time Variance Reduced Estimators
................658
16.4
Control
Variâtes
.........................................669
16.5
HP Variance Reduction
..................................677
16.6
Exercises
...............................................694
17
Trees and Markov Chain Approximations
..................697
17.1
Numerical Effects of Tree Methods
........................697
17.2
Efficiency of Simplified Schemes
...........................712
17.3
Higher Order Markov Chain Approximations
................720
17.4
Finite Difference Methods
................................734
17.5
Convergence Theorem for Markov Chains
...................744
17.6
Exercises
...............................................753
18
Solutions for Exercises
.....................................755
Acknowledgements
............................................781
Contents XIII
Bibliographical Notes
..........................................783
References
.....................................................793
Author Index
..................................................835
Index
..........................................................847
|
| any_adam_object | 1 |
| author | Platen, Eckhard 1949- Bruti-Liberati, Nicola 1975-2007 |
| author_GND | (DE-588)115479201 (DE-588)1311349863 |
| author_facet | Platen, Eckhard 1949- Bruti-Liberati, Nicola 1975-2007 |
| author_role | aut aut |
| author_sort | Platen, Eckhard 1949- |
| author_variant | e p ep n b l nbl |
| building | Verbundindex |
| bvnumber | BV036579317 |
| classification_rvk | SK 820 ST 610 |
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| ctrlnum | (OCoLC)699784257 (DE-599)BVBBV036579317 |
| dewey-full | 519.22 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.22 |
| dewey-search | 519.22 |
| dewey-sort | 3519.22 |
| dewey-tens | 510 - Mathematics |
| discipline | Informatik Mathematik Wirtschaftswissenschaften |
| format | Book |
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| id | DE-604.BV036579317 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:43:20Z |
| institution | BVB |
| isbn | 9783642120572 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-020500264 |
| oclc_num | 699784257 |
| open_access_boolean | |
| owner | DE-19 DE-BY-UBM DE-83 DE-11 DE-824 DE-739 DE-91G DE-BY-TUM DE-188 |
| owner_facet | DE-19 DE-BY-UBM DE-83 DE-11 DE-824 DE-739 DE-91G DE-BY-TUM DE-188 |
| physical | XXVIII, 856 Seiten graph. Darst. |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Springer |
| record_format | marc |
| series | Stochastic modelling and applied probability |
| series2 | Stochastic modelling and applied probability |
| spelling | Platen, Eckhard 1949- Verfasser (DE-588)115479201 aut Numerical solution of stochastic differential equations with jumps in finance Eckard Platen ; Nicola Bruti-Liberati Berlin [u.a.] Springer 2010 XXVIII, 856 Seiten graph. Darst. txt rdacontent n rdamedia nc rdacarrier Stochastic modelling and applied probability 64 Stochastische Differentialgleichung (DE-588)4057621-8 gnd rswk-swf Finanzmathematik (DE-588)4017195-4 gnd rswk-swf Zeitdiskrete Approximation (DE-588)4401310-3 gnd rswk-swf Monte-Carlo-Simulation (DE-588)4240945-7 gnd rswk-swf Poisson-Prozess (DE-588)4174971-6 gnd rswk-swf Stochastische Differentialgleichung (DE-588)4057621-8 s Poisson-Prozess (DE-588)4174971-6 s Zeitdiskrete Approximation (DE-588)4401310-3 s Monte-Carlo-Simulation (DE-588)4240945-7 s Finanzmathematik (DE-588)4017195-4 s DE-604 Bruti-Liberati, Nicola 1975-2007 Verfasser (DE-588)1311349863 aut Erscheint auch als Online-Ausgabe 978-3-642-13694-8 Stochastic modelling and applied probability 64 (DE-604)BV019623501 64 Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020500264&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Platen, Eckhard 1949- Bruti-Liberati, Nicola 1975-2007 Numerical solution of stochastic differential equations with jumps in finance Stochastic modelling and applied probability Stochastische Differentialgleichung (DE-588)4057621-8 gnd Finanzmathematik (DE-588)4017195-4 gnd Zeitdiskrete Approximation (DE-588)4401310-3 gnd Monte-Carlo-Simulation (DE-588)4240945-7 gnd Poisson-Prozess (DE-588)4174971-6 gnd |
| subject_GND | (DE-588)4057621-8 (DE-588)4017195-4 (DE-588)4401310-3 (DE-588)4240945-7 (DE-588)4174971-6 |
| title | Numerical solution of stochastic differential equations with jumps in finance |
| title_auth | Numerical solution of stochastic differential equations with jumps in finance |
| title_exact_search | Numerical solution of stochastic differential equations with jumps in finance |
| title_full | Numerical solution of stochastic differential equations with jumps in finance Eckard Platen ; Nicola Bruti-Liberati |
| title_fullStr | Numerical solution of stochastic differential equations with jumps in finance Eckard Platen ; Nicola Bruti-Liberati |
| title_full_unstemmed | Numerical solution of stochastic differential equations with jumps in finance Eckard Platen ; Nicola Bruti-Liberati |
| title_short | Numerical solution of stochastic differential equations with jumps in finance |
| title_sort | numerical solution of stochastic differential equations with jumps in finance |
| topic | Stochastische Differentialgleichung (DE-588)4057621-8 gnd Finanzmathematik (DE-588)4017195-4 gnd Zeitdiskrete Approximation (DE-588)4401310-3 gnd Monte-Carlo-Simulation (DE-588)4240945-7 gnd Poisson-Prozess (DE-588)4174971-6 gnd |
| topic_facet | Stochastische Differentialgleichung Finanzmathematik Zeitdiskrete Approximation Monte-Carlo-Simulation Poisson-Prozess |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020500264&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV019623501 |
| work_keys_str_mv | AT plateneckhard numericalsolutionofstochasticdifferentialequationswithjumpsinfinance AT brutiliberatinicola numericalsolutionofstochasticdifferentialequationswithjumpsinfinance |