Advanced stochastic models, risk assessment, and portfolio optimization: the ideal risk, uncertainty, and performance measures
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Hoboken, NJ
Wiley
2008
|
| Series: | The Frank J. Fabozzi series
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVIII, 382 S. graph. Darst. |
| ISBN: | 9780470053164 |
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MARC
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| 100 | 1 | |a Račev, Svetlozar T. |d 1951- |e Verfasser |0 (DE-588)12022979X |4 aut | |
| 245 | 1 | 0 | |a Advanced stochastic models, risk assessment, and portfolio optimization |b the ideal risk, uncertainty, and performance measures |c Svetlozar T. Rachev ; Stoyan V. Stoyanov ; Frank J. Fabozzi |
| 264 | 1 | |a Hoboken, NJ |b Wiley |c 2008 | |
| 300 | |a XVIII, 382 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a The Frank J. Fabozzi series | |
| 650 | 4 | |a Stochastischer Prozess / Mathematische Optimierung / Risikomanagement / Value at Risk / Portfolio-Management / Performance Measurement | |
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Mathematical optimization | |
| 650 | 4 | |a Portfolio management |x Mathematical models | |
| 650 | 4 | |a Risk assessment |x Mathematical models | |
| 650 | 4 | |a Stochastic processes | |
| 650 | 0 | 7 | |a Risikoanalyse |0 (DE-588)4137042-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Stochastisches Modell |0 (DE-588)4057633-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Portfolio Selection |0 (DE-588)4046834-3 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Portfolio Selection |0 (DE-588)4046834-3 |D s |
| 689 | 0 | 1 | |a Risikoanalyse |0 (DE-588)4137042-9 |D s |
| 689 | 0 | 2 | |a Stochastisches Modell |0 (DE-588)4057633-4 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Stoyanov, Stoyan Veselinov |e Verfasser |4 aut | |
| 700 | 1 | |a Fabozzi, Frank J. |d 1948- |e Verfasser |0 (DE-588)129772054 |4 aut | |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016483120&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-016483120 | ||
Record in the Search Index
| _version_ | 1804137625641025536 |
|---|---|
| adam_text | Contents
Preface
xiii
Acknowledgments
xv
About the Authors
xvii
CHAPTER
1
1
1.1
Introduction
1
1.2
Basic Concepts
2
1.3
Discrete Probability Distributions
2
1.3.1
Bernoulli Distribution
3
1.3.2
Binomial Distribution
3
1.3.3
Poisson
Distribution
4
1.4
Continuous Probability Distributions
5
1.4.1
Probability Distribution Function, Probability
Density Function, and Cumulative Distribution
Function
5
1.4.2
The Normal Distribution
8
1.4.3
Exponential Distribution
10
1.4.4
Student s
ŕ-distribution
11
1.4.5
Extreme Value Distribution
12
1.4.6
Generalized Extreme Value Distribution
12
1.5
Statistical Moments and Quantiles
13
1.5.1
Location
13
1.5.2
Dispersion
13
1.5.3
Asymmetry
13
1.5.4
Concentration in Tails
14
1.5.5
Statistical Moments
14
1.5.6
Quantiles
16
1.5.7
Sample Moments
16
1.6
Joint Probability Distributions
17
1.6.1
Conditional Probability
18
1.6.2
Definition of Joint Probability Distributions
19
¥1
1.6.3
Marginal Distributions
1.6.4
Dependence of Random Variables
1.6.5
Covariance and Correlation
1.6.6
Multivariate Normal Distribution
1.6.7
Elliptical Distributions
1.6.8
Copula Functions
1.7
Probabilistic Inequalities
1.7.1
Chebyshev s Inequality
1.7.2
Fréchet-Hoeffding
Inequality
1.8
Summary
CHAPTBt
2
Optimization
2.1
Introduction
2.2
Unconstrained ODtimization
Viii
CONTENTS
19
20
20
21
23
25
30
30
31
32
35
35
36
2.2.1
Minima and Maxima of a Differentiable
Function
37
2.2.2
Convex Functions
40
2.2.3
Quasiconvex Functions
46
2.3
Constrained Optimization
48
2.3.1 Lagrange
Multipliers
49
2.3.2
Convex Programming
52
2.3.3
Linear Programming
55
2.3.4
Quadratic Programming
57
2.4
Summary
58
61
61
62
63
64
68
72
73
74
75
84
86
3.4
Summary
90
3.5
Technical Appendix
90
снАРтаз
Probabi
Иу
Met
...
ntoo
3.1
Introduction
3.2
Measuring Distances: The Discrete Case
3.2.1
Sets of Characteristics
3.2.2
Distribution Functions
3.2.3
Joint Distribution
3.3
Primary, Simple, and Compound Metrics
3.3.1
Axiomatic Construction
3.3.2
Primary Metrics
3.3.3
Simple Metrics
3.3.4
Compound Metrics
3.3.5
Minimal and Maximal Metrics
Contents
ЇХ
3.5.1
Remarks on the Axiomatic Construction of
Probability Metrics
91
3.5.2
Examples of Probability Distances
94
3.5.3
Minimal and Maximal Distances
99
СНДРТВН
Ideal Probability Metrics
103
4.1
Introduction
103
4.2
The Classical Central Limit Theorem
105
4.2.1
The Binomial Approximation to the Normal
Distribution
105
4.2.2
The General Case
112
4.2.3
Estimating the Distance from the Limit
Distribution
118
4.3
The Generalized Central Limit Theorem
120
4.3.1
Stable Distributions
120
4.3.2
Modeling Financial Assets with Stable
Distributions
122
4.4
Construction of Ideal Probability Metrics
124
4.4.1
Definition
125
4.4.2
Examples
126
4.5
Summary
131
4.6
Technical Appendix
131
4.6.1
The CLT Conditions
131
4.6.2
Remarks on Ideal Metrics
133
CHAPTERS
Chotee
linden Uncertainty
1
за
5.1
Introduction
139
5.2
Expected Utility Theory
141
5.2.1
St. Petersburg Paradox
141
5.2.2
The
von Neumann-Morgenstern
Expected
Utility Theory
143
5.2.3
Types of Utility Functions
145
5.3
Stochastic Dominance
147
5.3.1
First-Order Stochastic Dominance
148
5.3.2
Second-Order Stochastic Dominance
149
5.3.3
Rothschild-Stiglitz Stochastic Dominance
150
5.3.4
Third-Order Stochastic Dominance
152
5.3.5
Efficient Sets and the Portfolio Choice Problem
154
5.3.6
Return versus Payoff
154
CONTENTS
5.4
Probability Metrics and Stochastic Dominance
157
5.5
Summary
161
5.6
Technical Appendix
161
5.6.1
The Axioms of Choice
161
5.6.2
Stochastic Dominance Relations of Order
η
163
5.6.3
Return versus Payoff and Stochastic Dominance
164
5.6.4
Other Stochastic Dominance Relations
166
CHflPTERß
Risk and Uncertainty
171
6.1
Introduction
171
6.2
Measures of Dispersion
174
6.2.1
Standard Deviation
174
6.2.2
Mean Absolute Deviation
176
6.2.3
Semistandard
Deviation
177
6.2.4
Axiomatic Description
178
6.2.5
Deviation Measures
179
6.3
Probability Metrics and Dispersion Measures
180
6.4
Measures of Risk
181
6.4.1
Value-at-Risk
182
6.4.2
Computing Portfolio VaR in Practice
186
6.4.3
Backtesting
of VaR
192
6.4.4
Coherent Risk Measures
194
6.5
Risk Measures and Dispersion Measures
198
6.6
Risk Measures and Stochastic Orders
199
6.7
Summary
200
6.8
Technical Appendix
201
6.8.1
Convex Risk Measures
201
6.8.2
Probability Metrics and Deviation Measures
202
CHAPTffiľ
Average Value-at-Risk
207
7.1
Introduction
207
7.2
Average Value-at-Risk
208
7.3
AVaR Estimation from a Sample
214
7.4
Computing Portfolio AVaR in Practice
216
7.4.1
The Multivariate Normal Assumption
216
7.4.2
The Historical Method
217
7.4.3
The Hybrid Method
217
7.4.4
The Monte Carlo Method
218
7.5
Backtesting
of AVaR
220
Contents Xi
7.6
Spectral
Risk Measures
222
7.7
Risk Measures and Probability Metrics
224
7.8
Summary
227
7.9
Technical Appendix
227
7.9.1
Characteristics of Conditional Loss
Distributions
228
7.9.2
Higher-Order AVaR
230
7.9.3
The Minimization Formula for AVaR
232
7.9.4
AVaR for Stable Distributions
235
7.9.5
ETL versus AVaR
236
7.9.6
Remarks on Spectral Risk Measures
241
CHAPTERS
Optimal Portfolios
245
8.1
Introduction
245
8.2
Mean-Variance Analysis
247
8.2.1
Mean-Variance Optimization Problems
247
8.2.2
The Mean-Variance Efficient Frontier
251
8.2.3
Mean-Variance Analysis and SSD
254
8.2.4
Adding a Risk-Free Asset
256
8.3
Mean-Risk Analysis
258
8.3.1
Mean-Risk Optimization Problems
259
8.3.2
The Mean-Risk Efficient Frontier
262
8.3.3
Mean-Risk Analysis and SSD
266
8.3.4
Risk versus Dispersion Measures
267
8.4
Summary
274
8.5
Technical Appendix
274
8.5.1
Types of Constraints
274
8.5.2
Quadratic Approximations to Utility Functions
276
8.5.3
Solving Mean-Variance Problems in Practice
278
8.5.4
Solving Mean-Risk Problems in Practice
279
8.5.5
Reward-Risk Analysis
281
СНАРШЭ
287
9.1
Introduction
287
9.2
The Tracking Error Problem
288
9.3
Relation to Probability Metrics
292
9.4
Examples of r.d. Metrics
296
9.5
Numerical Example
300
9.6
Summary
304
Xii________________________________________________________________
CONTENTS
9.7
Technical Appendix
304
9.7.1
Deviation Measures and r.d. Metrics
305
9.7.2
Remarks on the Axioms
305
9.7.3
Minimal r.d. Metrics
307
9.7.4
Limit Cases of C*p(X, Y) and
Θ;(Χ, Υ)
310
9.7.5
Computing r.d. Metrics in Practice
311
CHAPTBtiO
Performance Measures
317
10.1
Introduction
317
10.2
Reward-to-Risk Ratios
318
10.2.1
RR Ratios and the Efficient Portfolios
320
10.2.2
Limitations in the Application of
Reward-to-Risk Ratios
324
10.2.3
The STARR
325
10.2.4
The Sortino Ratio
329
10.2.5
The Sortino-Satchell Ratio
330
10.2.6
A One-Sided Variability Ratio
331
10.2.7
The Rachev Ratio
332
10.3
Reward-to-Variability Ratios
333
10.3.1
RV Ratios and the Efficient Portfolios
335
10.3.2
The
Sharpe
Ratio
337
10.3.3
The Capital Market Line and the
Sharpe
Ratio
340
10.4
Summary
343
10.5
Technical Appendix
343
10.5.1
Extensions of STARR
343
10.5.2
Quasiconcave Performance Measures
345
10.5.3
The Capital Market Line and Quasiconcave
Ratios
353
10.5.4
Nonquasiconcave Performance Measures
356
10.5.5
Probability Metrics and Performance Measures
357
|
| adam_txt |
Contents
Preface
xiii
Acknowledgments
xv
About the Authors
xvii
CHAPTER
1
1
1.1
Introduction
1
1.2
Basic Concepts
2
1.3
Discrete Probability Distributions
2
1.3.1
Bernoulli Distribution
3
1.3.2
Binomial Distribution
3
1.3.3
Poisson
Distribution
4
1.4
Continuous Probability Distributions
5
1.4.1
Probability Distribution Function, Probability
Density Function, and Cumulative Distribution
Function
5
1.4.2
The Normal Distribution
8
1.4.3
Exponential Distribution
10
1.4.4
Student's
ŕ-distribution
11
1.4.5
Extreme Value Distribution
12
1.4.6
Generalized Extreme Value Distribution
12
1.5
Statistical Moments and Quantiles
13
1.5.1
Location
13
1.5.2
Dispersion
13
1.5.3
Asymmetry
13
1.5.4
Concentration in Tails
14
1.5.5
Statistical Moments
14
1.5.6
Quantiles
16
1.5.7
Sample Moments
16
1.6
Joint Probability Distributions
17
1.6.1
Conditional Probability
18
1.6.2
Definition of Joint Probability Distributions
19
¥1
1.6.3
Marginal Distributions
1.6.4
Dependence of Random Variables
1.6.5
Covariance and Correlation
1.6.6
Multivariate Normal Distribution
1.6.7
Elliptical Distributions
1.6.8
Copula Functions
1.7
Probabilistic Inequalities
1.7.1
Chebyshev's Inequality
1.7.2
Fréchet-Hoeffding
Inequality
1.8
Summary
CHAPTBt
2
Optimization
2.1
Introduction
2.2
Unconstrained ODtimization
Viii
CONTENTS
19
20
20
21
23
25
30
30
31
32
35
35
36
2.2.1
Minima and Maxima of a Differentiable
Function
37
2.2.2
Convex Functions
40
2.2.3
Quasiconvex Functions
46
2.3
Constrained Optimization
48
2.3.1 Lagrange
Multipliers
49
2.3.2
Convex Programming
52
2.3.3
Linear Programming
55
2.3.4
Quadratic Programming
57
2.4
Summary
58
61
61
62
63
64
68
72
73
74
75
84
86
3.4
Summary
90
3.5
Technical Appendix
90
снАРтаз
Probabi
Иу
Met
.
ntoo
3.1
Introduction
3.2
Measuring Distances: The Discrete Case
3.2.1
Sets of Characteristics
3.2.2
Distribution Functions
3.2.3
Joint Distribution
3.3
Primary, Simple, and Compound Metrics
3.3.1
Axiomatic Construction
3.3.2
Primary Metrics
3.3.3
Simple Metrics
3.3.4
Compound Metrics
3.3.5
Minimal and Maximal Metrics
Contents
ЇХ
3.5.1
Remarks on the Axiomatic Construction of
Probability Metrics
91
3.5.2
Examples of Probability Distances
94
3.5.3
Minimal and Maximal Distances
99
СНДРТВН
Ideal Probability Metrics
103
4.1
Introduction
103
4.2
The Classical Central Limit Theorem
105
4.2.1
The Binomial Approximation to the Normal
Distribution
105
4.2.2
The General Case
112
4.2.3
Estimating the Distance from the Limit
Distribution
118
4.3
The Generalized Central Limit Theorem
120
4.3.1
Stable Distributions
120
4.3.2
Modeling Financial Assets with Stable
Distributions
122
4.4
Construction of Ideal Probability Metrics
124
4.4.1
Definition
125
4.4.2
Examples
126
4.5
Summary
131
4.6
Technical Appendix
131
4.6.1
The CLT Conditions
131
4.6.2
Remarks on Ideal Metrics
133
CHAPTERS
Chotee
linden Uncertainty
1
за
5.1
Introduction
139
5.2
Expected Utility Theory
141
5.2.1
St. Petersburg Paradox
141
5.2.2
The
von Neumann-Morgenstern
Expected
Utility Theory
143
5.2.3
Types of Utility Functions
145
5.3
Stochastic Dominance
147
5.3.1
First-Order Stochastic Dominance
148
5.3.2
Second-Order Stochastic Dominance
149
5.3.3
Rothschild-Stiglitz Stochastic Dominance
150
5.3.4
Third-Order Stochastic Dominance
152
5.3.5
Efficient Sets and the Portfolio Choice Problem
154
5.3.6
Return versus Payoff
154
CONTENTS
5.4
Probability Metrics and Stochastic Dominance
157
5.5
Summary
161
5.6
Technical Appendix
161
5.6.1
The Axioms of Choice
161
5.6.2
Stochastic Dominance Relations of Order
η
163
5.6.3
Return versus Payoff and Stochastic Dominance
164
5.6.4
Other Stochastic Dominance Relations
166
CHflPTERß
Risk and Uncertainty
171
6.1
Introduction
171
6.2
Measures of Dispersion
174
6.2.1
Standard Deviation
174
6.2.2
Mean Absolute Deviation
176
6.2.3
Semistandard
Deviation
177
6.2.4
Axiomatic Description
178
6.2.5
Deviation Measures
179
6.3
Probability Metrics and Dispersion Measures
180
6.4
Measures of Risk
181
6.4.1
Value-at-Risk
182
6.4.2
Computing Portfolio VaR in Practice
186
6.4.3
Backtesting
of VaR
192
6.4.4
Coherent Risk Measures
194
6.5
Risk Measures and Dispersion Measures
198
6.6
Risk Measures and Stochastic Orders
199
6.7
Summary
200
6.8
Technical Appendix
201
6.8.1
Convex Risk Measures
201
6.8.2
Probability Metrics and Deviation Measures
202
CHAPTffiľ
Average Value-at-Risk
207
7.1
Introduction
207
7.2
Average Value-at-Risk
208
7.3
AVaR Estimation from a Sample
214
7.4
Computing Portfolio AVaR in Practice
216
7.4.1
The Multivariate Normal Assumption
216
7.4.2
The Historical Method
217
7.4.3
The Hybrid Method
217
7.4.4
The Monte Carlo Method
218
7.5
Backtesting
of AVaR
220
Contents Xi
7.6
Spectral
Risk Measures
222
7.7
Risk Measures and Probability Metrics
224
7.8
Summary
227
7.9
Technical Appendix
227
7.9.1
Characteristics of Conditional Loss
Distributions
228
7.9.2
Higher-Order AVaR
230
7.9.3
The Minimization Formula for AVaR
232
7.9.4
AVaR for Stable Distributions
235
7.9.5
ETL versus AVaR
236
7.9.6
Remarks on Spectral Risk Measures
241
CHAPTERS
Optimal Portfolios
245
8.1
Introduction
245
8.2
Mean-Variance Analysis
247
8.2.1
Mean-Variance Optimization Problems
247
8.2.2
The Mean-Variance Efficient Frontier
251
8.2.3
Mean-Variance Analysis and SSD
254
8.2.4
Adding a Risk-Free Asset
256
8.3
Mean-Risk Analysis
258
8.3.1
Mean-Risk Optimization Problems
259
8.3.2
The Mean-Risk Efficient Frontier
262
8.3.3
Mean-Risk Analysis and SSD
266
8.3.4
Risk versus Dispersion Measures
267
8.4
Summary
274
8.5
Technical Appendix
274
8.5.1
Types of Constraints
274
8.5.2
Quadratic Approximations to Utility Functions
276
8.5.3
Solving Mean-Variance Problems in Practice
278
8.5.4
Solving Mean-Risk Problems in Practice
279
8.5.5
Reward-Risk Analysis
281
СНАРШЭ
287
9.1
Introduction
287
9.2
The Tracking Error Problem
288
9.3
Relation to Probability Metrics
292
9.4
Examples of r.d. Metrics
296
9.5
Numerical Example
300
9.6
Summary
304
Xii_
CONTENTS
9.7
Technical Appendix
304
9.7.1
Deviation Measures and r.d. Metrics
305
9.7.2
Remarks on the Axioms
305
9.7.3
Minimal r.d. Metrics
307
9.7.4
Limit Cases of C*p(X, Y) and
Θ;(Χ, Υ)
310
9.7.5
Computing r.d. Metrics in Practice
311
CHAPTBtiO
Performance Measures
317
10.1
Introduction
317
10.2
Reward-to-Risk Ratios
318
10.2.1
RR Ratios and the Efficient Portfolios
320
10.2.2
Limitations in the Application of
Reward-to-Risk Ratios
324
10.2.3
The STARR
325
10.2.4
The Sortino Ratio
329
10.2.5
The Sortino-Satchell Ratio
330
10.2.6
A One-Sided Variability Ratio
331
10.2.7
The Rachev Ratio
332
10.3
Reward-to-Variability Ratios
333
10.3.1
RV Ratios and the Efficient Portfolios
335
10.3.2
The
Sharpe
Ratio
337
10.3.3
The Capital Market Line and the
Sharpe
Ratio
340
10.4
Summary
343
10.5
Technical Appendix
343
10.5.1
Extensions of STARR
343
10.5.2
Quasiconcave Performance Measures
345
10.5.3
The Capital Market Line and Quasiconcave
Ratios
353
10.5.4
Nonquasiconcave Performance Measures
356
10.5.5
Probability Metrics and Performance Measures
357 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Račev, Svetlozar T. 1951- Stoyanov, Stoyan Veselinov Fabozzi, Frank J. 1948- |
| author_GND | (DE-588)12022979X (DE-588)129772054 |
| author_facet | Račev, Svetlozar T. 1951- Stoyanov, Stoyan Veselinov Fabozzi, Frank J. 1948- |
| author_role | aut aut aut |
| author_sort | Račev, Svetlozar T. 1951- |
| author_variant | s t r st str s v s sv svs f j f fj fjf |
| building | Verbundindex |
| bvnumber | BV023298631 |
| callnumber-first | H - Social Science |
| callnumber-label | HG4529 |
| callnumber-raw | HG4529.5 |
| callnumber-search | HG4529.5 |
| callnumber-sort | HG 44529.5 |
| callnumber-subject | HG - Finance |
| classification_rvk | QH 237 QH 440 QK 810 SK 980 |
| ctrlnum | (OCoLC)254292446 (DE-599)BVBBV023298631 |
| dewey-full | 332.60151923 |
| dewey-hundreds | 300 - Social sciences |
| dewey-ones | 332 - Financial economics |
| dewey-raw | 332.60151923 |
| dewey-search | 332.60151923 |
| dewey-sort | 3332.60151923 |
| dewey-tens | 330 - Economics |
| discipline | Mathematik Wirtschaftswissenschaften |
| discipline_str_mv | Mathematik Wirtschaftswissenschaften |
| format | Book |
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| id | DE-604.BV023298631 |
| illustrated | Illustrated |
| index_date | 2024-07-02T20:45:39Z |
| indexdate | 2024-07-09T21:15:16Z |
| institution | BVB |
| isbn | 9780470053164 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016483120 |
| oclc_num | 254292446 |
| open_access_boolean | |
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| owner_facet | DE-355 DE-BY-UBR DE-29T DE-1050 DE-945 DE-11 DE-1051 DE-188 DE-473 DE-BY-UBG |
| physical | XVIII, 382 S. graph. Darst. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Wiley |
| record_format | marc |
| series2 | The Frank J. Fabozzi series |
| spelling | Račev, Svetlozar T. 1951- Verfasser (DE-588)12022979X aut Advanced stochastic models, risk assessment, and portfolio optimization the ideal risk, uncertainty, and performance measures Svetlozar T. Rachev ; Stoyan V. Stoyanov ; Frank J. Fabozzi Hoboken, NJ Wiley 2008 XVIII, 382 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier The Frank J. Fabozzi series Stochastischer Prozess / Mathematische Optimierung / Risikomanagement / Value at Risk / Portfolio-Management / Performance Measurement Mathematisches Modell Mathematical optimization Portfolio management Mathematical models Risk assessment Mathematical models Stochastic processes Risikoanalyse (DE-588)4137042-9 gnd rswk-swf Stochastisches Modell (DE-588)4057633-4 gnd rswk-swf Portfolio Selection (DE-588)4046834-3 gnd rswk-swf Portfolio Selection (DE-588)4046834-3 s Risikoanalyse (DE-588)4137042-9 s Stochastisches Modell (DE-588)4057633-4 s DE-604 Stoyanov, Stoyan Veselinov Verfasser aut Fabozzi, Frank J. 1948- Verfasser (DE-588)129772054 aut Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016483120&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Račev, Svetlozar T. 1951- Stoyanov, Stoyan Veselinov Fabozzi, Frank J. 1948- Advanced stochastic models, risk assessment, and portfolio optimization the ideal risk, uncertainty, and performance measures Stochastischer Prozess / Mathematische Optimierung / Risikomanagement / Value at Risk / Portfolio-Management / Performance Measurement Mathematisches Modell Mathematical optimization Portfolio management Mathematical models Risk assessment Mathematical models Stochastic processes Risikoanalyse (DE-588)4137042-9 gnd Stochastisches Modell (DE-588)4057633-4 gnd Portfolio Selection (DE-588)4046834-3 gnd |
| subject_GND | (DE-588)4137042-9 (DE-588)4057633-4 (DE-588)4046834-3 |
| title | Advanced stochastic models, risk assessment, and portfolio optimization the ideal risk, uncertainty, and performance measures |
| title_auth | Advanced stochastic models, risk assessment, and portfolio optimization the ideal risk, uncertainty, and performance measures |
| title_exact_search | Advanced stochastic models, risk assessment, and portfolio optimization the ideal risk, uncertainty, and performance measures |
| title_exact_search_txtP | Advanced stochastic models, risk assessment, and portfolio optimization the ideal risk, uncertainty, and performance measures |
| title_full | Advanced stochastic models, risk assessment, and portfolio optimization the ideal risk, uncertainty, and performance measures Svetlozar T. Rachev ; Stoyan V. Stoyanov ; Frank J. Fabozzi |
| title_fullStr | Advanced stochastic models, risk assessment, and portfolio optimization the ideal risk, uncertainty, and performance measures Svetlozar T. Rachev ; Stoyan V. Stoyanov ; Frank J. Fabozzi |
| title_full_unstemmed | Advanced stochastic models, risk assessment, and portfolio optimization the ideal risk, uncertainty, and performance measures Svetlozar T. Rachev ; Stoyan V. Stoyanov ; Frank J. Fabozzi |
| title_short | Advanced stochastic models, risk assessment, and portfolio optimization |
| title_sort | advanced stochastic models risk assessment and portfolio optimization the ideal risk uncertainty and performance measures |
| title_sub | the ideal risk, uncertainty, and performance measures |
| topic | Stochastischer Prozess / Mathematische Optimierung / Risikomanagement / Value at Risk / Portfolio-Management / Performance Measurement Mathematisches Modell Mathematical optimization Portfolio management Mathematical models Risk assessment Mathematical models Stochastic processes Risikoanalyse (DE-588)4137042-9 gnd Stochastisches Modell (DE-588)4057633-4 gnd Portfolio Selection (DE-588)4046834-3 gnd |
| topic_facet | Stochastischer Prozess / Mathematische Optimierung / Risikomanagement / Value at Risk / Portfolio-Management / Performance Measurement Mathematisches Modell Mathematical optimization Portfolio management Mathematical models Risk assessment Mathematical models Stochastic processes Risikoanalyse Stochastisches Modell Portfolio Selection |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016483120&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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