The concepts and practice of mathematical finance:
An ideal introduction for those starting out as practitioners of mathematical finance, this book provides a clear understanding of the intuition behind derivatives pricing, how models are implemented, and how they are used and adapted in practice. Strengths and weaknesses of different models, e.g. B...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
2008
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Mathematics, finance and risk
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Zusammenfassung: | An ideal introduction for those starting out as practitioners of mathematical finance, this book provides a clear understanding of the intuition behind derivatives pricing, how models are implemented, and how they are used and adapted in practice. Strengths and weaknesses of different models, e.g. Black-Scholes, stochastic volatility, jump-diffusion and variance gamma, are examined. Both the theory and the implementation of the industry-standard LIBOR market model are considered in detail. Each pricing problem is approached using multiple techniques including the well-known PDE and martingale approaches. This second edition contains many more worked examples and over 200 exercises with detailed solutions. Extensive appendices provide a guide to jargon, a recap of the elements of probability theory, and a collection of computer projects. The author brings to this book a blend of practical experience and rigorous mathematical background and supplies here the working knowledge needed to become a good quantitative analyst. |
| Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke Includes bibliographical references and index |
| Beschreibung: | XVIII, 539 S. graph. Darst. |
| ISBN: | 9780521514088 |
Internformat
MARC
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| 100 | 1 | |a Joshi, Mark S. |d 1969- |e Verfasser |0 (DE-588)12898693X |4 aut | |
| 245 | 1 | 0 | |a The concepts and practice of mathematical finance |c M. S. Joshi |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2008 | |
| 300 | |a XVIII, 539 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Mathematics, finance and risk | |
| 500 | |a Hier auch später erschienene, unveränderte Nachdrucke | ||
| 500 | |a Includes bibliographical references and index | ||
| 520 | 3 | |a An ideal introduction for those starting out as practitioners of mathematical finance, this book provides a clear understanding of the intuition behind derivatives pricing, how models are implemented, and how they are used and adapted in practice. Strengths and weaknesses of different models, e.g. Black-Scholes, stochastic volatility, jump-diffusion and variance gamma, are examined. Both the theory and the implementation of the industry-standard LIBOR market model are considered in detail. Each pricing problem is approached using multiple techniques including the well-known PDE and martingale approaches. This second edition contains many more worked examples and over 200 exercises with detailed solutions. Extensive appendices provide a guide to jargon, a recap of the elements of probability theory, and a collection of computer projects. The author brings to this book a blend of practical experience and rigorous mathematical background and supplies here the working knowledge needed to become a good quantitative analyst. | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Derivative securities |x Prices |x Mathematical models | |
| 650 | 4 | |a Options (Finance) |x Prices |x Mathematical models | |
| 650 | 4 | |a Interest rates |x Mathematical models | |
| 650 | 4 | |a Finance |x Mathematical models | |
| 650 | 4 | |a Investments |x Mathematics | |
| 650 | 4 | |a Risk management |x Mathematical models | |
| 650 | 0 | 7 | |a Finanzmathematik |0 (DE-588)4017195-4 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Finanzmathematik |0 (DE-588)4017195-4 |D s |
| 689 | 0 | |C b |5 DE-604 | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-016761084 | ||
Datensatz im Suchindex
| _version_ | 1804138050971762688 |
|---|---|
| adam_text | Contents
Preface
Acknowledgements
1
Risk
1.1
What is risk?
1.2
Market efficiency
1.3
The most important assets
1.4
Risk diversification and hedging
1.5
The use of options
1.6
Classifying market participants
1.7
Key points
1.8
Further reading
1.9
Exercises
2
Pricing methodologies and arbitrage
2.1
Some possible methodologies
2.2
Delta hedging
2.3
What is arbitrage?
2.4
The assumptions of mathematical finance
2.5
An example of arbitrage-free pricing
2.6
The time value of money
2.7
Mathematically defining arbitrage
2.8
Using arbitrage to bound option prices
2.9
Conclusion
2.10
Key points
2.11
Further reading
2.12
Exercises
3
Trees
and option pricing
3.1
A two-world universe
3.2
A three-state model
page
xiv
xviii
1
1
2
4
12
13
14
14
16
16
18
19
20
22
24
27
29
39
39
39
40
44
44
49
VII
viii Contents
3.3
Multiple time steps
50
3.4
Many time steps
53
3.5
A normal model
55
3.6
Putting interest rates in
58
3.7
A log-normal model
60
3.8
Consequences
68
3.9
Summary
70
3.10
Key points
70
3.11
Further reading
71
3.12
Exercises
71
Practicalities
73
4.1
Introduction
73
4.2
Trading volatility
73
4.3
Smiles
74
4.4
The Greeks
77
4.5
Alternative models
85
4.6
Transaction costs
90
4.7
Key points
90
4.8
Further reading
91
4.9
Exercises
91
The
Ito
calculus
97
5.1
Introduction
97
5.2
Brownian motion
97
5.3
Quadratic variation
100
5.4
Stochastic processes
102
5.5
Ito s lemma
106
5.6
Applying Ito s lemma
111
5.7
An informal derivation of the Black-Scholes equation
114
5.8
Justifying the derivation
116
5.9
Solving the Black-Scholes equation
119
5.10
Dividend-paying assets
121
5.11
Key points
123
5.12
Further reading
125
5.13
Exercises
125
Risk neutrality and martingale measures
127
6.1
Plan
127
6.2
Introduction
128
6.3
The existence of risk-neutral measures
129
6.4
The concept of information
140
6.5
Discrete martingale pricing
145
Contents ix
6.6
Continuous
martingales
and nitrations
154
6.7
Identifying continuous martingales
156
6.8
Continuous martingale pricing
157
6.9
Equivalence to the PDE method
161
6.10
Hedging
162
6.11
Time-dependent parameters
164
6.12
Completeness and uniqueness
166
6.13
Changing numeraire
167
6.14
Dividend-paying assets
171
6.15
Working with the forward
172
6.16
Key points
175
6.17
Further reading
176
6.18
Exercises
176
The practical pricing of a European option
181
7.1
Introduction
181
7.2
Analytic formulae
182
183
187
191
195
196
198
198
199
202
202
205
207
208
210
213
216
219
220
220
220
222
222
223
225
7.3
Trees
7.4
Numerical integration
7.5
Monte Carlo
7.6
PDE methods
7.7
Replication
7.8
Key points
7.9
Further reading
7.10
Exercises
Continuous barrier options
8.1
Introduction
8.2
The PDE pricing of continuous barrier options
8.3
Expectation pricing of continuous barrier options
8.4
The reflection principle
8.5
Girsanov s theorem revisited
8.6
Joint distribution
8.7
Pricing continuous barriers by expectation
8.8
American digital options
8.9
Key points
8.10
Further reading
8.11
Exercises
Multi-look exotic options
9.1
Introduction
9.2
Risk-neutral pricing for path-dependent options
9.3
Weak path dependence
Contents
226
231
233
234
236
239
239
240
10
Static
replication
243
243
244
247
249
251
252
256
258
259
11
Multiple sources of risk
260
260
261
263
267
272
273
275
277
280
281
281
12
Options with early exercise features
284
284
287
289
291
293
295
297
297
298
9.4
Path generation and dimensionality reduction
9.5
Moment matching
9.6
Trees, PDEs and Asian options
9.7
Practical issues in pricing multi-look options
9.8
Greeks of multi-look options
9.9
Key points
9.10
Further reading
9.11
Exercises
Static
ι
•eplication
10.1
Introduction
10.2
Continuous barrier options
10.3
Discrete barriers
10.4
Path-dependent exotic options
10.5
The up-and-in put with barrier at strike
10.6
Put-call symmetry
10.7
Conclusion and further reading
10.8
Key points
10.9
Exercises
Multiple sources of risk
11.1
Introduction
11.2
Higher-dimensional Brownian motions
11.3
The higher-dimensional
Ito
calculus
11.4
The higher-dimensional Girsanov theorem
11.5
Practical pricing
11.6
The
Margrabe
option
11.7
Quanto
options
11.8
Higher-dimensional trees
11.9
Key points
11.10
Further reading
11.11
Exercises
Options with early exercise features
12.1
Introduction
12.2
The tree approach
12.3
The PDE approach to American options
12.4
American options by replication
12.5
American options by Monte Carlo
12.6
Upper bounds by Monte Carlo
12.7
Key points
12.8
Further reading
12.9
Exercises
Contents xi
13
Interest
rate derivatives 300
13.1
Introduction
300
13.2
The simplest instruments
302
13.3
Caplets and swaptions
309
13.4
Curves and more curves
314
13.5
Key points
316
13.6
Further reading
317
13.7
Exercises
317
14
The pricing of exotic interest rate derivatives
319
14.1
Introduction
319
14.2
Decomposing an instrument into forward rates
323
14.3
Computing the drift of a forward rate
330
14.4
The instantaneous volatility curves
333
14.5
The instantaneous correlations between forward
rates
335
14.6
Doing the simulation
337
14.7
Rapid pricing of swaptions in a BGM model
340
14.8
Automatic calibration to co-terminal swaptions
342
14.9
Lower bounds for
Bermudán
swaptions
345
14.10
Upper bounds for
Bermudán
swaptions
349
14.11
Factor reduction and
Bermudán
swaptions
352
14.12
Interest-rate smiles
355
14.13
Key points
358
14.14
Further reading
358
14.15
Exercises
359
15
Incomplete markets and jump-diffusion processes
361
15.1
Introduction
361
15.2
Modelling jumps with a tree
362
15.3
Modelling jumps in a continuous framework
364
15.4
Market incompleteness
367
15.5
Super- and sub-replication
369
15.6
Choosing the measure and hedging exotic options
375
15.7
Matching the market
377
15.8
Pricing exotic options using jump-diffusion
models
379
15.9
Does the model matter?
381
15.10
Log-type models
382
15.11
Key points
385
15.12
Further reading
386
15.13
Exercises
387
xii Contents
16
17
18
Stochastic volatility
389
16.1
Introduction
389
16.2
Risk-neutral pricing with stochastic-volatility models
390
16.3
Monte Carlo and stochastic volatility
391
16.4
Hedging issues
393
16.5
PDE pricing and transform methods
395
16.6
Stochastic volatility smiles
398
16.7
Pricing exotic options
398
16.8
Key points
399
16.9
Further reading
399
16.10
Exercises
400
Variance Gamma models
401
17.1
The Variance Gamma process
401
17.2
Pricing options with Variance Gamma models
404
17.3
Pricing exotic options with Variance Gamma models
407
17.4
Deriving the properties
408
17.5
Key points
410
17.6
Further reading
410
17.7
Exercises
411
Smile
dynamics and the pricing of exotic options
412
18.1
Introduction
412
18.2
Smile dynamics in the market
413
18.3
Dynamics implied by models
415
18.4
Matching the smile to the model
421
18.5
Hedging
424
18.6
Matching the model to the product
425
18.7
Key points
427
18.8
Further reading
428
Appendix A Financial and mathematical jargon
429
Appendix
В
Computer projects
434
B.I
Introduction
434
B.2
Two important functions
435
B.3
Project
1 :
Vanilla options in a Black-Scholes world
437
B.4
Project
2:
Vanilla Greeks
440
B.5
Project
3:
Hedging
441
B.6
Project
4:
Recombining trees
443
B.7
Project
5:
Exotic options by Monte Carlo
444
B.8
Project
6:
Using low-discrepancy numbers
445
B.9
Project
7:
Replication models for continuous barrier options
447
B.10
Proiect
8:
Multi-asset options
448
Contents xiii
В.
11
Project
9:
Simple
interest-rate derivative pricing
448
В.
12
Project
10:
LIBOR-in-arrears
449
В.
13
Project
11:
BGM
450
B.14 Project
12:
Jump-diffusion models
454
B.15 Project
13:
Stochastic volatility
455
B.16 Project
14:
Variance Gamma
456
AppendixC Elements of probability theory
458
C.I Definitions
458
C.2 Expectations and moments
462
C.3 Joint density and distribution functions
464
C.4 Covariances and correlations
466
Appendix
D
Order notation
469
D.I Big
Ό
469
D.2
Smallo
471
Appendix
E
Hints and answers to exercises
472
References
526
Index
533
|
| adam_txt |
Contents
Preface
Acknowledgements
1
Risk
1.1
What is risk?
1.2
Market efficiency
1.3
The most important assets
1.4
Risk diversification and hedging
1.5
The use of options
1.6
Classifying market participants
1.7
Key points
1.8
Further reading
1.9
Exercises
2
Pricing methodologies and arbitrage
2.1
Some possible methodologies
2.2
Delta hedging
2.3
What is arbitrage?
2.4
The assumptions of mathematical finance
2.5
An example of arbitrage-free pricing
2.6
The time value of money
2.7
Mathematically defining arbitrage
2.8
Using arbitrage to bound option prices
2.9
Conclusion
2.10
Key points
2.11
Further reading
2.12
Exercises
3
Trees
and option pricing
3.1
A two-world universe
3.2
A three-state model
page
xiv
xviii
1
1
2
4
12
13
14
14
16
16
18
19
20
22
24
27
29
39
39
39
40
44
44
49
VII
viii Contents
3.3
Multiple time steps
50
3.4
Many time steps
53
3.5
A normal model
55
3.6
Putting interest rates in
58
3.7
A log-normal model
60
3.8
Consequences
68
3.9
Summary
70
3.10
Key points
70
3.11
Further reading
71
3.12
Exercises
71
Practicalities
73
4.1
Introduction
73
4.2
Trading volatility
73
4.3
Smiles
74
4.4
The Greeks
77
4.5
Alternative models
85
4.6
Transaction costs
90
4.7
Key points
90
4.8
Further reading
91
4.9
Exercises
91
The
Ito
calculus
97
5.1
Introduction
97
5.2
Brownian motion
97
5.3
Quadratic variation
100
5.4
Stochastic processes
102
5.5
Ito's lemma
106
5.6
Applying Ito's lemma
111
5.7
An informal derivation of the Black-Scholes equation
114
5.8
Justifying the derivation
116
5.9
Solving the Black-Scholes equation
119
5.10
Dividend-paying assets
121
5.11
Key points
123
5.12
Further reading
125
5.13
Exercises
125
Risk neutrality and martingale measures
127
6.1
Plan
127
6.2
Introduction
128
6.3
The existence of risk-neutral measures
129
6.4
The concept of information
140
6.5
Discrete martingale pricing
145
Contents ix
6.6
Continuous
martingales
and nitrations
154
6.7
Identifying continuous martingales
156
6.8
Continuous martingale pricing
157
6.9
Equivalence to the PDE method
161
6.10
Hedging
162
6.11
Time-dependent parameters
164
6.12
Completeness and uniqueness
166
6.13
Changing numeraire
167
6.14
Dividend-paying assets
171
6.15
Working with the forward
172
6.16
Key points
175
6.17
Further reading
176
6.18
Exercises
176
The practical pricing of a European option
181
7.1
Introduction
181
7.2
Analytic formulae
182
183
187
191
195
196
198
198
199
202
202
205
207
208
210
213
216
219
220
220
220
222
222
223
225
7.3
Trees
7.4
Numerical integration
7.5
Monte Carlo
7.6
PDE methods
7.7
Replication
7.8
Key points
7.9
Further reading
7.10
Exercises
Continuous barrier options
8.1
Introduction
8.2
The PDE pricing of continuous barrier options
8.3
Expectation pricing of continuous barrier options
8.4
The reflection principle
8.5
Girsanov's theorem revisited
8.6
Joint distribution
8.7
Pricing continuous barriers by expectation
8.8
American digital options
8.9
Key points
8.10
Further reading
8.11
Exercises
Multi-look exotic options
9.1
Introduction
9.2
Risk-neutral pricing for path-dependent options
9.3
Weak path dependence
Contents
226
231
233
234
236
239
239
240
10
Static
replication
243
243
244
247
249
251
252
256
258
259
11
Multiple sources of risk
260
260
261
263
267
272
273
275
277
280
281
281
12
Options with early exercise features
284
284
287
289
291
293
295
297
297
298
9.4
Path generation and dimensionality reduction
9.5
Moment matching
9.6
Trees, PDEs and Asian options
9.7
Practical issues in pricing multi-look options
9.8
Greeks of multi-look options
9.9
Key points
9.10
Further reading
9.11
Exercises
Static
ι
•eplication
10.1
Introduction
10.2
Continuous barrier options
10.3
Discrete barriers
10.4
Path-dependent exotic options
10.5
The up-and-in put with barrier at strike
10.6
Put-call symmetry
10.7
Conclusion and further reading
10.8
Key points
10.9
Exercises
Multiple sources of risk
11.1
Introduction
11.2
Higher-dimensional Brownian motions
11.3
The higher-dimensional
Ito
calculus
11.4
The higher-dimensional Girsanov theorem
11.5
Practical pricing
11.6
The
Margrabe
option
11.7
Quanto
options
11.8
Higher-dimensional trees
11.9
Key points
11.10
Further reading
11.11
Exercises
Options with early exercise features
12.1
Introduction
12.2
The tree approach
12.3
The PDE approach to American options
12.4
American options by replication
12.5
American options by Monte Carlo
12.6
Upper bounds by Monte Carlo
12.7
Key points
12.8
Further reading
12.9
Exercises
Contents xi
13
Interest
rate derivatives 300
13.1
Introduction
300
13.2
The simplest instruments
302
13.3
Caplets and swaptions
309
13.4
Curves and more curves
314
13.5
Key points
316
13.6
Further reading
317
13.7
Exercises
317
14
The pricing of exotic interest rate derivatives
319
14.1
Introduction
319
14.2
Decomposing an instrument into forward rates
323
14.3
Computing the drift of a forward rate
330
14.4
The instantaneous volatility curves
333
14.5
The instantaneous correlations between forward
rates
335
14.6
Doing the simulation
337
14.7
Rapid pricing of swaptions in a BGM model
340
14.8
Automatic calibration to co-terminal swaptions
342
14.9
Lower bounds for
Bermudán
swaptions
345
14.10
Upper bounds for
Bermudán
swaptions
349
14.11
Factor reduction and
Bermudán
swaptions
352
14.12
Interest-rate smiles
355
14.13
Key points
358
14.14
Further reading
358
14.15
Exercises
359
15
Incomplete markets and jump-diffusion processes
361
15.1
Introduction
361
15.2
Modelling jumps with a tree
362
15.3
Modelling jumps in a continuous framework
364
15.4
Market incompleteness
367
15.5
Super- and sub-replication
369
15.6
Choosing the measure and hedging exotic options
375
15.7
Matching the market
377
15.8
Pricing exotic options using jump-diffusion
models
379
15.9
Does the model matter?
381
15.10
Log-type models
382
15.11
Key points
385
15.12
Further reading
386
15.13
Exercises
387
xii Contents
16
17
18
Stochastic volatility
389
16.1
Introduction
389
16.2
Risk-neutral pricing with stochastic-volatility models
390
16.3
Monte Carlo and stochastic volatility
391
16.4
Hedging issues
393
16.5
PDE pricing and transform methods
395
16.6
Stochastic volatility smiles
398
16.7
Pricing exotic options
398
16.8
Key points
399
16.9
Further reading
399
16.10
Exercises
400
Variance Gamma models
401
17.1
The Variance Gamma process
401
17.2
Pricing options with Variance Gamma models
404
17.3
Pricing exotic options with Variance Gamma models
407
17.4
Deriving the properties
408
17.5
Key points
410
17.6
Further reading
410
17.7
Exercises
411
Smile
dynamics and the pricing of exotic options
412
18.1
Introduction
412
18.2
Smile dynamics in the market
413
18.3
Dynamics implied by models
415
18.4
Matching the smile to the model
421
18.5
Hedging
424
18.6
Matching the model to the product
425
18.7
Key points
427
18.8
Further reading
428
Appendix A Financial and mathematical jargon
429
Appendix
В
Computer projects
434
B.I
Introduction
434
B.2
Two important functions
435
B.3
Project
1 :
Vanilla options in a Black-Scholes world
437
B.4
Project
2:
Vanilla Greeks
440
B.5
Project
3:
Hedging
441
B.6
Project
4:
Recombining trees
443
B.7
Project
5:
Exotic options by Monte Carlo
444
B.8
Project
6:
Using low-discrepancy numbers
445
B.9
Project
7:
Replication models for continuous barrier options
447
B.10
Proiect
8:
Multi-asset options
448
Contents xiii
В.
11
Project
9:
Simple
interest-rate derivative pricing
448
В.
12
Project
10:
LIBOR-in-arrears
449
В.
13
Project
11:
BGM
450
B.14 Project
12:
Jump-diffusion models
454
B.15 Project
13:
Stochastic volatility
455
B.16 Project
14:
Variance Gamma
456
AppendixC Elements of probability theory
458
C.I Definitions
458
C.2 Expectations and moments
462
C.3 Joint density and distribution functions
464
C.4 Covariances and correlations
466
Appendix
D
Order notation
469
D.I Big
Ό
469
D.2
Smallo
471
Appendix
E
Hints and answers to exercises
472
References
526
Index
533 |
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| discipline | Mathematik Wirtschaftswissenschaften |
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| spelling | Joshi, Mark S. 1969- Verfasser (DE-588)12898693X aut The concepts and practice of mathematical finance M. S. Joshi 2. ed. Cambridge [u.a.] Cambridge Univ. Press 2008 XVIII, 539 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematics, finance and risk Hier auch später erschienene, unveränderte Nachdrucke Includes bibliographical references and index An ideal introduction for those starting out as practitioners of mathematical finance, this book provides a clear understanding of the intuition behind derivatives pricing, how models are implemented, and how they are used and adapted in practice. Strengths and weaknesses of different models, e.g. Black-Scholes, stochastic volatility, jump-diffusion and variance gamma, are examined. Both the theory and the implementation of the industry-standard LIBOR market model are considered in detail. Each pricing problem is approached using multiple techniques including the well-known PDE and martingale approaches. This second edition contains many more worked examples and over 200 exercises with detailed solutions. Extensive appendices provide a guide to jargon, a recap of the elements of probability theory, and a collection of computer projects. The author brings to this book a blend of practical experience and rigorous mathematical background and supplies here the working knowledge needed to become a good quantitative analyst. Mathematik Mathematisches Modell Derivative securities Prices Mathematical models Options (Finance) Prices Mathematical models Interest rates Mathematical models Finance Mathematical models Investments Mathematics Risk management Mathematical models Finanzmathematik (DE-588)4017195-4 gnd rswk-swf Finanzmathematik (DE-588)4017195-4 s b DE-604 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016761084&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Joshi, Mark S. 1969- The concepts and practice of mathematical finance Mathematik Mathematisches Modell Derivative securities Prices Mathematical models Options (Finance) Prices Mathematical models Interest rates Mathematical models Finance Mathematical models Investments Mathematics Risk management Mathematical models Finanzmathematik (DE-588)4017195-4 gnd |
| subject_GND | (DE-588)4017195-4 |
| title | The concepts and practice of mathematical finance |
| title_auth | The concepts and practice of mathematical finance |
| title_exact_search | The concepts and practice of mathematical finance |
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| title_full | The concepts and practice of mathematical finance M. S. Joshi |
| title_fullStr | The concepts and practice of mathematical finance M. S. Joshi |
| title_full_unstemmed | The concepts and practice of mathematical finance M. S. Joshi |
| title_short | The concepts and practice of mathematical finance |
| title_sort | the concepts and practice of mathematical finance |
| topic | Mathematik Mathematisches Modell Derivative securities Prices Mathematical models Options (Finance) Prices Mathematical models Interest rates Mathematical models Finance Mathematical models Investments Mathematics Risk management Mathematical models Finanzmathematik (DE-588)4017195-4 gnd |
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