Stochastic processes and financial mathematics:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin
Springer
[2023]
|
| Schriftenreihe: | Mathematics study resources
volume 1 |
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | ix, 304 Seiten Illustrationen |
| ISBN: | 9783662647103 3662647109 |
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| 100 | 1 | |a Rüschendorf, Ludger |d 1948- |e Verfasser |0 (DE-588)10867472X |4 aut | |
| 245 | 1 | 0 | |a Stochastic processes and financial mathematics |c Ludger Rüschendorf |
| 264 | 1 | |a Berlin |b Springer |c [2023] | |
| 264 | 4 | |c © 2023 | |
| 300 | |a ix, 304 Seiten |b Illustrationen | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Mathematics study resources |v volume 1 | |
| 653 | |a Option valuation in complete markets | ||
| 653 | |a Option valuation in incomplete markets | ||
| 653 | |a Skorohod embedding theorem | ||
| 653 | |a Donskert theorem | ||
| 653 | |a Option pricing | ||
| 653 | |a Stochastic integral | ||
| 653 | |a Martingale | ||
| 653 | |a Itô formula | ||
| 653 | |a Stochastic Analysis | ||
| 653 | |a Hedging strategies | ||
| 653 | |a Benefit optimization | ||
| 653 | |a Time constant models | ||
| 653 | |a Black-Scholes model | ||
| 710 | 2 | |a Springer-Verlag GmbH |0 (DE-588)1065168780 |4 pbl | |
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| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-033996987 | |
Datensatz im Suchindex
| _version_ | 1817968279943118848 |
|---|---|
| adam_text |
CONTENTS
1
OPTION
PRICING
IN
DISCRETE
TIME
MODELS
.
1
2
SKOROHOD
'
S
EMBEDDING
THEOREM
AND
DONSKER
'
S
THEOREM
.
11
2.1
SKOROHOD
'
S
EMBEDDING
THEOREM
.
11
2.2
FUNCTIONAL
LIMIT
THEOREM
.
19
3
STOCHASTIC
INTEGRATION
.
27
3.1
MARTINGALES
AND
PREDICTABLE
PROCESSES
.
27
3.2
LTD
INTEGRAL
FOR
THE
BROWNIAN
MOTION
.
40
3.2.1
EXTENSION
OF
THE
INTEGRAL
TO
L2-INTEGRANDS
.
43
3.2.2
CONSTRUCTION
OF
THE
INTEGRAL
FOR
CO(B)
.
48
3.3
QUADRATIC
VARIATION
OF
CONTINUOUS
LOCAL
MARTINGALES
.
55
3.4
STOCHASTIC
INTEGRAL
OF
CONTINUOUS
LOCAL
MARTINGALES
.
71
3.4.1
STOCHASTIC
INTEGRAL
FOR
CONTINUOUS
L
2
-MARTINGALES
.
71
3.4.2
EXTENSION
TO
THE
SET
OF
CONTINUOUS
LOCAL
MARTINGALES
.
76
3.4.3
EXTENSION
TO
THE
CASE
OF
CONTINUOUS
SEMIMARTINGALES
.
79
3.5
INTEGRATION
OF
SEMIMARTINGALES
.
82
3.5.1
DECOMPOSITION
THEOREMS
.
84
3.5.2
STOCHASTIC
INTEGRAL
FOR
ME
.
86
3.5.3
STOCHASTIC
INTEGRAL FOR
SEMIMARTINGALES
.
87
4
ELEMENTS
OF
STOCHASTIC
ANALYSIS
.
95
4.1
LTD
FORMULA
.
95
4.2
MARTINGALE
REPRESENTATION
.
117
4.3
MEASURE
CHANGE,
THEOREM
OF
GIRSANOV
.
132
4.3.1
APPLICATIONS
OF
THE
GIRSANOV
THEOREM
.
145
4.3.2
THE
CLARK
FORMULA
.
149
4.4
STOCHASTIC
DIFFERENTIAL
EQUATIONS
.
152
4.4.1
STRONG
SOLUTION
-
WEAK
SOLUTION
OF
STOCHASTIC
DIFFERENTIAL
EQUATIONS
.
165
4.5
SEMIGROUP,
PDE,
AND
SDE
APPROACH
TO
DIFFUSION
PROCESSES
.
173
5
OPTION
PRICES
IN
COMPLETE
AND
INCOMPLETE
MARKETS
.
191
5.1
THE
BLACK-SCHOLES
MODEL
AND
RISK-NEUTRAL
VALUATION
.
192
5.1.1
RISK-NEUTRAL
VALUATION
OF
OPTIONS
.
199
5.1.2
DISCUSSION
OF
THE
BLACK-SCHOLES
FORMULA
.
206
VI
CONTENTS
5.1.3
HEDGING
STRATEGIES
AND
PARTIAL
DIFFERENTIAL
EQUATIONS
.
216
5.2
COMPLETE
AND
INCOMPLETE
MARKETS
.
219
6
UTILITY
OPTIMIZATION,
MINIMUM
DISTANCE
MARTINGALE
MEASURES,
AND
UTILITY
INDIFFERENCE
PRICING
.
233
6.1
UTILITY
OPTIMIZATION
AND
UTILITY
INDIFFERENCE
PRICING
.
233
6.2
MINIMUM
DISTANCE
MARTINGALE
MEASURES
.
235
6.3
DUALITY
RESULTS
.
242
6.3.1
MINIMUM
DISTANCE
MARTINGALE
MEASURES
AND
MINIMAX
MEASURES
.
242
6.3.2
RELATIONSHIP
TO
PORTFOLIO
OPTIMIZATION
.
250
6.4
UTILITY-BASED
HEDGING
.
255
6.5
EXAMPLES
IN
EXPONENTIAL
LEVY
MODELS
.
263
6.6
PROPERTIES
OF
THE
UTILITY
INDIFFERENCE
PRICE
.
269
7
VARIANCE-MINIMAL
HEDGING
.
279
7.1
HEDGING
IN
THE
MARTINGALE
CASE
.
280
7.2
HEDGING
IN
THE
SEMIMARTINGALE
CASE
.
284
7.2.1
FOLLMER-SCHWEIZER
DECOMPOSITION
AND
OPTIMALITY
EQUATION
.
285
7.2.2 MINIMAL
MARTINGALE
MEASURES
AND
OPTIMAL
STRATEGIES
.
288
BIBLIOGRAPHY
.
295
INDEX
.
299 |
| adam_txt |
CONTENTS
1
OPTION
PRICING
IN
DISCRETE
TIME
MODELS
.
1
2
SKOROHOD
'
S
EMBEDDING
THEOREM
AND
DONSKER
'
S
THEOREM
.
11
2.1
SKOROHOD
'
S
EMBEDDING
THEOREM
.
11
2.2
FUNCTIONAL
LIMIT
THEOREM
.
19
3
STOCHASTIC
INTEGRATION
.
27
3.1
MARTINGALES
AND
PREDICTABLE
PROCESSES
.
27
3.2
LTD
INTEGRAL
FOR
THE
BROWNIAN
MOTION
.
40
3.2.1
EXTENSION
OF
THE
INTEGRAL
TO
L2-INTEGRANDS
.
43
3.2.2
CONSTRUCTION
OF
THE
INTEGRAL
FOR
CO(B)
.
48
3.3
QUADRATIC
VARIATION
OF
CONTINUOUS
LOCAL
MARTINGALES
.
55
3.4
STOCHASTIC
INTEGRAL
OF
CONTINUOUS
LOCAL
MARTINGALES
.
71
3.4.1
STOCHASTIC
INTEGRAL
FOR
CONTINUOUS
L
2
-MARTINGALES
.
71
3.4.2
EXTENSION
TO
THE
SET
OF
CONTINUOUS
LOCAL
MARTINGALES
.
76
3.4.3
EXTENSION
TO
THE
CASE
OF
CONTINUOUS
SEMIMARTINGALES
.
79
3.5
INTEGRATION
OF
SEMIMARTINGALES
.
82
3.5.1
DECOMPOSITION
THEOREMS
.
84
3.5.2
STOCHASTIC
INTEGRAL
FOR
ME
.
86
3.5.3
STOCHASTIC
INTEGRAL FOR
SEMIMARTINGALES
.
87
4
ELEMENTS
OF
STOCHASTIC
ANALYSIS
.
95
4.1
LTD
FORMULA
.
95
4.2
MARTINGALE
REPRESENTATION
.
117
4.3
MEASURE
CHANGE,
THEOREM
OF
GIRSANOV
.
132
4.3.1
APPLICATIONS
OF
THE
GIRSANOV
THEOREM
.
145
4.3.2
THE
CLARK
FORMULA
.
149
4.4
STOCHASTIC
DIFFERENTIAL
EQUATIONS
.
152
4.4.1
STRONG
SOLUTION
-
WEAK
SOLUTION
OF
STOCHASTIC
DIFFERENTIAL
EQUATIONS
.
165
4.5
SEMIGROUP,
PDE,
AND
SDE
APPROACH
TO
DIFFUSION
PROCESSES
.
173
5
OPTION
PRICES
IN
COMPLETE
AND
INCOMPLETE
MARKETS
.
191
5.1
THE
BLACK-SCHOLES
MODEL
AND
RISK-NEUTRAL
VALUATION
.
192
5.1.1
RISK-NEUTRAL
VALUATION
OF
OPTIONS
.
199
5.1.2
DISCUSSION
OF
THE
BLACK-SCHOLES
FORMULA
.
206
VI
CONTENTS
5.1.3
HEDGING
STRATEGIES
AND
PARTIAL
DIFFERENTIAL
EQUATIONS
.
216
5.2
COMPLETE
AND
INCOMPLETE
MARKETS
.
219
6
UTILITY
OPTIMIZATION,
MINIMUM
DISTANCE
MARTINGALE
MEASURES,
AND
UTILITY
INDIFFERENCE
PRICING
.
233
6.1
UTILITY
OPTIMIZATION
AND
UTILITY
INDIFFERENCE
PRICING
.
233
6.2
MINIMUM
DISTANCE
MARTINGALE
MEASURES
.
235
6.3
DUALITY
RESULTS
.
242
6.3.1
MINIMUM
DISTANCE
MARTINGALE
MEASURES
AND
MINIMAX
MEASURES
.
242
6.3.2
RELATIONSHIP
TO
PORTFOLIO
OPTIMIZATION
.
250
6.4
UTILITY-BASED
HEDGING
.
255
6.5
EXAMPLES
IN
EXPONENTIAL
LEVY
MODELS
.
263
6.6
PROPERTIES
OF
THE
UTILITY
INDIFFERENCE
PRICE
.
269
7
VARIANCE-MINIMAL
HEDGING
.
279
7.1
HEDGING
IN
THE
MARTINGALE
CASE
.
280
7.2
HEDGING
IN
THE
SEMIMARTINGALE
CASE
.
284
7.2.1
FOLLMER-SCHWEIZER
DECOMPOSITION
AND
OPTIMALITY
EQUATION
.
285
7.2.2 MINIMAL
MARTINGALE
MEASURES
AND
OPTIMAL
STRATEGIES
.
288
BIBLIOGRAPHY
.
295
INDEX
.
299 |
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| id | DE-604.BV048621798 |
| illustrated | Illustrated |
| index_date | 2024-07-03T21:13:52Z |
| indexdate | 2024-12-09T13:07:35Z |
| institution | BVB |
| institution_GND | (DE-588)1065168780 |
| isbn | 9783662647103 3662647109 |
| language | English |
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| open_access_boolean | |
| owner | DE-11 |
| owner_facet | DE-11 |
| physical | ix, 304 Seiten Illustrationen |
| publishDate | 2023 |
| publishDateSearch | 2023 |
| publishDateSort | 2023 |
| publisher | Springer |
| record_format | marc |
| series | Mathematics study resources |
| series2 | Mathematics study resources |
| spelling | Rüschendorf, Ludger 1948- Verfasser (DE-588)10867472X aut Stochastic processes and financial mathematics Ludger Rüschendorf Berlin Springer [2023] © 2023 ix, 304 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Mathematics study resources volume 1 Option valuation in complete markets Option valuation in incomplete markets Skorohod embedding theorem Donskert theorem Option pricing Stochastic integral Martingale Itô formula Stochastic Analysis Hedging strategies Benefit optimization Time constant models Black-Scholes model Springer-Verlag GmbH (DE-588)1065168780 pbl Erscheint auch als Online-Ausgabe 978-3-662-64711-0 Mathematics study resources volume 1 (DE-604)BV048913706 1 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=8194279d88b6468aa58c6637714b3088&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=033996987&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Rüschendorf, Ludger 1948- Stochastic processes and financial mathematics Mathematics study resources |
| title | Stochastic processes and financial mathematics |
| title_auth | Stochastic processes and financial mathematics |
| title_exact_search | Stochastic processes and financial mathematics |
| title_exact_search_txtP | Stochastic processes and financial mathematics |
| title_full | Stochastic processes and financial mathematics Ludger Rüschendorf |
| title_fullStr | Stochastic processes and financial mathematics Ludger Rüschendorf |
| title_full_unstemmed | Stochastic processes and financial mathematics Ludger Rüschendorf |
| title_short | Stochastic processes and financial mathematics |
| title_sort | stochastic processes and financial mathematics |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=8194279d88b6468aa58c6637714b3088&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=033996987&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV048913706 |
| work_keys_str_mv | AT ruschendorfludger stochasticprocessesandfinancialmathematics AT springerverlaggmbh stochasticprocessesandfinancialmathematics |