Statistical tools in finance and insurance:
Gespeichert in:
| Weitere Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin
Springer
2004
|
| Ausgabe: | 1. Ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 400 S. 235 mm x 155 mm |
| ISBN: | 3540221891 |
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| 084 | |a 330 |2 sdnb | ||
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| 245 | 1 | 0 | |a Statistical tools in finance and insurance |c Hrsg. Pavel Cizek ... |
| 250 | |a 1. Ed. | ||
| 264 | 1 | |a Berlin |b Springer |c 2004 | |
| 300 | |a 400 S. |c 235 mm x 155 mm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Assurance - Méthodes statistiques | |
| 650 | 4 | |a Finances - Méthodes statistiques | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Finance |x Mathematical models | |
| 650 | 4 | |a Insurance |x Mathematics | |
| 650 | 0 | 7 | |a Versicherungsmathematik |0 (DE-588)4063194-1 |2 gnd |9 rswk-swf |
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| 700 | 1 | |a Čížek, Pavel |0 (DE-588)129834866 |4 edt | |
| 856 | 4 | 2 | |m DNB Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013060788&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
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Datensatz im Suchindex
| _version_ | 1804133197099827200 |
|---|---|
| adam_text | CONTENTS
CONTRIBUTORS
13
PREFACE
15
I
FINANCE
19
1
STABLE
DISTRIBUTIONS
21
SZYMON
BORAK,
WOLFGANG
HARDLE,
AND
RAFA L
WERON
1.1
INTRODUCTION
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21
1.2
DEYYNITIONS
AND
BASIC
CHARACTERISTIC
.
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22
1.2.1
CHARACTERISTIC
FUNCTION
REPRESENTATION
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24
1.2.2
STABLE
DENSITY
AND
DISTRIBUTION
FUNCTIONS
.
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26
1.3
SIMULATION
OF
YY
-STABLE
VARIABLES
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28
1.4
ESTIMATION
OF
PARAMETERS
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30
1.4.1
TAIL
EXPONENT
ESTIMATION
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31
1.4.2
QUANTILE
ESTIMATION
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33
1.4.3
CHARACTERISTIC
FUNCTION
APPROACHES
.
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34
1.4.4
MAXIMUM
LIKELIHOOD
METHOD
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35
1.5
FINANCIAL
APPLICATIONS
OF
STABLE
LAWS
.
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36
2
CONTENTS
2
EXTREME
VALUE
ANALYSIS
AND
COPULAS
45
KRZYSZTOF
JAJUGA
AND
DANIEL
PAPLA
2.1
INTRODUCTION
.
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45
2.1.1
ANALYSIS
OF
DISTRIBUTION
OF
THE
EXTREMUM
.
.
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46
2.1.2
ANALYSIS
OF
CONDITIONAL
EXCESS
DISTRIBUTION
.
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47
2.1.3
EXAMPLES
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48
2.2
MULTIVARIATE
TIME
SERIES
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53
2.2.1
COPULA
APPROACH
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53
2.2.2
EXAMPLES
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56
2.2.3
MULTIVARIATE
EXTREME
VALUE
APPROACH
.
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57
2.2.4
EXAMPLES
.
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60
2.2.5
COPULA
ANALYSIS
FOR
MULTIVARIATE
TIME
SERIES
.
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61
2.2.6
EXAMPLES
.
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62
3
TAIL
DEPENDENCE
65
RAFAEL
SCHMIDT
3.1
INTRODUCTION
.
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65
3.2
WHAT
IS
TAIL
DEPENDENCE?
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66
3.3
CALCULATION
OF
THE
TAIL-DEPENDENCE
COEYYCIENT
.
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69
3.3.1
ARCHIMEDEAN
COPULAE
.
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69
3.3.2
ELLIPTICALLY-CONTOURED
DISTRIBUTIONS
.
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70
3.3.3
OTHER
COPULAE
.
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74
3.4
ESTIMATING
THE
TAIL-DEPENDENCE
COEYYCIENT
.
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75
3.5
COMPARISON
OF
TDC
ESTIMATORS
.
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78
3.6
TAIL
DEPENDENCE
OF
ASSET
AND
FX
RETURNS
.
.
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81
3.7
VALUE
AT
RISK
{
A
SIMULATION
STUDY
.
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84
CONTENTS
3
4
PRICING
OF
CATASTROPHE
BONDS
93
KRZYSZTOF
BURNECKI,
GRZEGORZ
KUKLA,
AND
DAVID
TAYLOR
4.1
INTRODUCTION
.
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93
4.1.1
THE
EMERGENCE
OF
CAT
BONDS
.
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94
4.1.2
INSURANCE
SECURITIZATION
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96
4.1.3
CAT
BOND
PRICING
METHODOLOGY
.
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97
4.2
COMPOUND
DOUBLY
STOCHASTIC
POISSON
PRICING
MODEL
.
.
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.
99
4.3
CALIBRATION
OF
THE
PRICING
MODEL
.
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100
4.4
DYNAMICS
OF
THE
CAT
BOND
PRICE
.
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104
5
COMMON
FUNCTIONAL
IV
ANALYSIS
115
MICHAL
BENKO
AND
WOLFGANG
HARDLE
5.1
INTRODUCTION
.
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115
5.2
IMPLIED
VOLATILITY
SURFACE
.
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116
5.3
FUNCTIONAL
DATA
ANALYSIS
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118
5.4
FUNCTIONAL
PRINCIPAL
COMPONENTS
.
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121
5.4.1
BASIS
EXPANSION
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123
5.5
SMOOTHED
PRINCIPAL
COMPONENTS
ANALYSIS
.
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125
5.5.1
BASIS
EXPANSION
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126
5.6
COMMON
PRINCIPAL
COMPONENTS
MODEL
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127
6
IMPLIED
TRINOMIAL
TREES
135
PAVEL
YY
CYYYYYYZEK
AND
KAREL
KOMORYYAD
6.1
OPTION
PRICING
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136
6.2
TREES
AND
IMPLIED
TREES
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138
6.3
IMPLIED
TRINOMIAL
TREES
.
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140
6.3.1
BASIC
INSIGHT
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140
4
CONTENTS
6.3.2
STATE
SPACE
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142
6.3.3
TRANSITION
PROBABILITIES
.
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144
6.3.4
POSSIBLE
PITFALLS
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145
6.4
EXAMPLES
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147
6.4.1
PRE-SPECIYYED
IMPLIED
VOLATILITY
.
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147
6.4.2
GERMAN
STOCK
INDEX
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152
7
HESTON S
MODEL
AND
THE
SMILE
161
RAFA L
WERON
AND
UWE
WYSTUP
7.1
INTRODUCTION
.
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161
7.2
HESTON S
MODEL
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163
7.3
OPTION
PRICING
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166
7.3.1
GREEKS
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168
7.4
CALIBRATION
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169
7.4.1
QUALITATIVE
EYYECTS
OF
CHANGING
PARAMETERS
.
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171
7.4.2
CALIBRATION
RESULTS
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173
8
FFT-BASED
OPTION
PRICING
183
SZYMON
BORAK,
KAI
DETLEFSEN,
AND
WOLFGANG
HARDLE
8.1
INTRODUCTION
.
.
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183
8.2
MODERN
PRICING
MODELS
.
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183
8.2.1
MERTON
MODEL
.
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184
8.2.2
HESTON
MODEL
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185
8.2.3
BATES
MODEL
.
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187
8.3
OPTION
PRICING
WITH
FFT
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188
8.4
APPLICATIONS
.
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192
CONTENTS
5
9
VALUATION
OF
MORTGAGE
BACKED
SECURITIES
201
NICOLAS
GAUSSEL
AND
JULIEN
TAMINE
9.1
INTRODUCTION
.
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201
9.2
OPTIMALLY
PREPAID
MORTGAGE
.
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204
9.2.1
FINANCIAL
CHARACTERISTICS
AND
CASH
FLOW
ANALYSIS
.
.
.
204
9.2.2
OPTIMAL
BEHAVIOR
AND
PRICE
.
.
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204
9.3
VALUATION
OF
MORTGAGE
BACKED
SECURITIES
.
.
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212
9.3.1
GENERIC
FRAMEWORK
.
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213
9.3.2
A
PARAMETRIC
SPECIYYCATION
OF
THE
PREPAYMENT
RATE
.
.
215
9.3.3
SENSITIVITY
ANALYSIS
.
.
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218
10
PREDICTING
BANKRUPTCY
WITH
SUPPORT
VECTOR
MACHINES
225
WOLFGANG
HARDLE,
ROUSLAN
MORO,
AND
DOROTHEA
SCHAFER
10.1
BANKRUPTCY
ANALYSIS
METHODOLOGY
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
226
10.2
IMPORTANCE
OF
RISK
CLASSIYYCATION
IN
PRACTICE
.
.
.
.
.
.
.
.
.
.
230
10.3
LAGRANGIAN
FORMULATION
OF
THE
SVM
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
233
10.4
DESCRIPTION
OF
DATA
.
.
.
.
.
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.
236
10.5
COMPUTATIONAL
RESULTS
.
.
.
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.
.
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.
237
10.6
CONCLUSIONS
.
.
.
.
.
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.
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.
.
.
.
.
243
11
MODELLING
INDONESIAN
MONEY
DEMAND
249
NOER
AZAM
ACHSANI,
OLIVER
HOLTEMOLLER,
AND
HIZIR
SOFYAN
11.1
SPECIYYCATION
OF
MONEY
DEMAND
FUNCTIONS
.
.
.
.
.
.
.
.
.
.
.
.
250
11.2
THE
ECONOMETRIC
APPROACH
TO
MONEY
DEMAND
.
.
.
.
.
.
.
.
.
253
11.2.1
ECONOMETRIC
ESTIMATION
OF
MONEY
DEMAND
FUNCTIONS
.
253
11.2.2
ECONOMETRIC
MODELLING
OF
INDONESIAN
MONEY
DEMAND
.
254
11.3
THE
FUZZY
APPROACH
TO
MONEY
DEMAND
.
.
.
.
.
.
.
.
.
.
.
.
.
260
6
CONTENTS
11.3.1
FUZZY
CLUSTERING
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
260
11.3.2
THE
TAKAGI-SUGENO
APPROACH
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
261
11.3.3
MODEL
IDENTIYYCATION
.
.
.
.
.
.
.
.
.
.
.
.
.
.
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.
.
.
.
.
262
11.3.4
FUZZY
MODELLING
OF
INDONESIAN
MONEY
DEMAND
.
.
.
.
.
263
11.4
CONCLUSIONS
.
.
.
.
.
.
.
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.
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.
266
12
NONPARAMETRIC
PRODUCTIVITY
ANALYSIS
271
WOLFGANG
HARDLE
AND
SEOK-OH
JEONG
12.1
THE
BASIC
CONCEPTS
.
.
.
.
.
.
.
.
.
.
.
.
.
.
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.
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.
272
12.2
NONPARAMETRIC
HULL
METHODS
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
276
12.2.1
DATA
ENVELOPMENT
ANALYSIS
.
.
.
.
.
.
.
.
.
.
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.
.
.
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.
277
12.2.2
FREE
DISPOSAL
HULL
.
.
.
.
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.
278
12.3
DEA
IN
PRACTICE:
INSURANCE
AGENCIES
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
279
12.4
FDH
IN
PRACTICE:
MANUFACTURING
INDUSTRY
.
.
.
.
.
.
.
.
.
.
.
.
281
II
INSURANCE
287
13
LOSS
DISTRIBUTIONS
289
KRZYSZTOF
BURNECKI,
ADAM
MISIOREK,
AND
RAFA L
WERON
13.1
INTRODUCTION
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
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.
.
.
.
.
289
13.2
EMPIRICAL
DISTRIBUTION
FUNCTION
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
290
13.3
ANALYTICAL
METHODS
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
292
13.3.1
LOG-NORMAL
DISTRIBUTION
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
292
13.3.2
EXPONENTIAL
DISTRIBUTION
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
293
13.3.3
PARETO
DISTRIBUTION
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
295
13.3.4
BURR
DISTRIBUTION
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
298
13.3.5
WEIBULL
DISTRIBUTION
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
298
CONTENTS
7
13.3.6
GAMMA
DISTRIBUTION
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
300
13.3.7
MIXTURE
OF
EXPONENTIAL
DISTRIBUTIONS
.
.
.
.
.
.
.
.
.
.
.
302
13.4
STATISTICAL
VALIDATION
TECHNIQUES
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
303
13.4.1
MEAN
EXCESS
FUNCTION
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
303
13.4.2
TESTS
BASED
ON
THE
EMPIRICAL
DISTRIBUTION
FUNCTION
.
.
305
13.4.3
LIMITED
EXPECTED
VALUE
FUNCTION
.
.
.
.
.
.
.
.
.
.
.
.
.
309
13.5
APPLICATIONS
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
311
14
MODELING
OF
THE
RISK
PROCESS
319
KRZYSZTOF
BURNECKI
AND
RAFA L
WERON
14.1
INTRODUCTION
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
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.
.
.
.
.
.
.
319
14.2
CLAIM
ARRIVAL
PROCESSES
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
321
14.2.1
HOMOGENEOUS
POISSON
PROCESS
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
321
14.2.2
NON-HOMOGENEOUS
POISSON
PROCESS
.
.
.
.
.
.
.
.
.
.
.
.
323
14.2.3
MIXED
POISSON
PROCESS
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
326
14.2.4
COX
PROCESS
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
327
14.2.5
RENEWAL
PROCESS
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
328
14.3
SIMULATION
OF
RISK
PROCESSES
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
329
14.3.1
CATASTROPHIC
LOSSES
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
329
14.3.2
DANISH
FIRE
LOSSES
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
334
15
RUIN
PROBABILITIES
IN
FINITE
AND
INYYNITE
TIME
341
KRZYSZTOF
BURNECKI,
PAWE L
MIYYSTA,
AND
ALEKSANDER
WERON
15.1
INTRODUCTION
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
341
15.1.1
LIGHT-
AND
HEAVY-TAILED
DISTRIBUTIONS
.
.
.
.
.
.
.
.
.
.
343
15.2
EXACT
RUIN
PROBABILITIES
IN
INYYNITE
TIME
.
.
.
.
.
.
.
.
.
.
.
.
346
15.2.1
NO
INITIAL
CAPITAL
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
347
8
CONTENTS
15.2.2
EXPONENTIAL
CLAIM
AMOUNTS
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
347
15.2.3
GAMMA
CLAIM
AMOUNTS
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
347
15.2.4
MIXTURE
OF
TWO
EXPONENTIALS
CLAIM
AMOUNTS
.
.
.
.
.
.
349
15.3
APPROXIMATIONS
OF
THE
RUIN
PROBABILITY
IN
INYYNITE
TIME
.
.
.
.
350
15.3.1
CRAMYYER{LUNDBERG
APPROXIMATION
.
.
.
.
.
.
.
.
.
.
.
.
351
15.3.2
EXPONENTIAL
APPROXIMATION
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
352
15.3.3
LUNDBERG
APPROXIMATION
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
352
15.3.4
BEEKMAN{BOWERS
APPROXIMATION
.
.
.
.
.
.
.
.
.
.
.
.
.
353
15.3.5
RENYI
APPROXIMATION
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
354
15.3.6
DE
VYLDER
APPROXIMATION
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
355
15.3.7
4-MOMENT
GAMMA
DE
VYLDER
APPROXIMATION
.
.
.
.
.
.
356
15.3.8
HEAVY
TRAYYC
APPROXIMATION
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
358
15.3.9
LIGHT
TRAYYC
APPROXIMATION
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
359
15.3.10HEAVY-LIGHT
TRAYYC
APPROXIMATION
.
.
.
.
.
.
.
.
.
.
.
.
360
15.3.11SUBEXPONENTIAL
APPROXIMATION
.
.
.
.
.
.
.
.
.
.
.
.
.
.
360
15.3.12COMPUTERAPPROXIMATIONVIATHEPOLLACZEK-KHINCHINFOR
MULA
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
361
15.3.13SUMMARY
OF
THE
APPROXIMATIONS
.
.
.
.
.
.
.
.
.
.
.
.
.
362
15.4
NUMERICAL
COMPARISON
OF
THE
INYYNITE
TIME
APPROXIMATIONS
.
.
363
15.5
EXACT
RUIN
PROBABILITIES
IN
FINITE
TIME
.
.
.
.
.
.
.
.
.
.
.
.
.
367
15.5.1
EXPONENTIAL
CLAIM
AMOUNTS
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
368
15.6
APPROXIMATIONS
OF
THE
RUIN
PROBABILITY
IN
FINITE
TIME
.
.
.
.
368
15.6.1
MONTE
CARLO
METHOD
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
369
15.6.2
SEGERDAHL
NORMAL
APPROXIMATION
.
.
.
.
.
.
.
.
.
.
.
.
.
369
15.6.3
DIYYUSION
APPROXIMATION
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
371
15.6.4
CORRECTED
DIYYUSION
APPROXIMATION
.
.
.
.
.
.
.
.
.
.
.
.
372
15.6.5
FINITE
TIME
DE
VYLDER
APPROXIMATION
.
.
.
.
.
.
.
.
.
.
373
CONTENTS
9
15.6.6
SUMMARY
OF
THE
APPROXIMATIONS
.
.
.
.
.
.
.
.
.
.
.
.
.
374
15.7
NUMERICAL
COMPARISON
OF
THE
FINITE
TIME
APPROXIMATIONS
.
.
374
16
STABLE
DIYYUSION
APPROXIMATION
OF
THE
RISK
PROCESS
381
HANSJORG
FURRER,
ZBIGNIEW
MICHNA,
AND
ALEKSANDER
WERON
16.1
INTRODUCTION
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
381
16.2
BROWNIAN
MOTION
AND
THE
RISK
MODEL
FOR
SMALL
CLAIMS
.
.
.
.
382
16.2.1
WEAK
CONVERGENCE
OF
RISK
PROCESSES
TO
BROWNIAN
MOTION
383
16.2.2
RUIN
PROBABILITY
FOR
THE
LIMIT
PROCESS
.
.
.
.
.
.
.
.
.
.
383
16.2.3
EXAMPLES
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
384
16.3
STABLE
LYYEVY
MOTION
AND
THE
RISK
MODEL
FOR
LARGE
CLAIMS
.
.
.
386
16.3.1
WEAK
CONVERGENCE
OF
RISK
PROCESSES
TO
YY
-STABLE
LYYEVY
MOTION
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
387
16.3.2
RUIN
PROBABILITY
IN
LIMIT
RISK
MODEL
FOR
LARGE
CLAIMS
388
16.3.3
EXAMPLES
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
390
17
RISK
MODEL
OF
GOOD
AND
BAD
PERIODS
395
ZBIGNIEW
MICHNA
17.1
INTRODUCTION
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
395
17.2
FRACTIONAL
BROWNIAN
MOTION
AND
MODEL
OF
GOOD
AND
BAD
PERIODS
396
17.3
RUIN
PROBABILITY
IN
LIMIT
RISK
MODEL
OF
GOOD
AND
BAD
PERIODS
399
17.4
EXAMPLES
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
402
18
PREMIUMS
IN
THE
INDIVIDUAL
AND
COLLECTIVE
RISK
MODELS
407
JAN
IWANIK
AND
JOANNA
NOWICKA-ZAGRAJEK
18.1
PREMIUM
CALCULATION
PRINCIPLES
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
408
18.2
INDIVIDUAL
RISK
MODEL
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
410
18.2.1
GENERAL
PREMIUM
FORMULAE
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
411
10
CONTENTS
18.2.2
PREMIUMS
IN
THE
CASE
OF
THE
NORMAL
APPROXIMATION
.
.
412
18.2.3
EXAMPLES
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
413
18.3
COLLECTIVE
RISK
MODEL
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
416
18.3.1
GENERAL
PREMIUM
FORMULAE
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
417
18.3.2
PREMIUMS
IN
THE
CASE
OF
THE
NORMAL
AND
TRANSLATED
GAMMA
APPROXIMATIONS
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
418
18.3.3
COMPOUND
POISSON
DISTRIBUTION
.
.
.
.
.
.
.
.
.
.
.
.
.
420
18.3.4
COMPOUND
NEGATIVE
BINOMIAL
DISTRIBUTION
.
.
.
.
.
.
.
421
18.3.5
EXAMPLES
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
423
19
PURE
RISK
PREMIUMS
UNDER
DEDUCTIBLES
427
KRZYSZTOF
BURNECKI,
JOANNA
NOWICKA-ZAGRAJEK,
AND
AGNIESZKA
WY LOMAYYNSKA
19.1
INTRODUCTION
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
427
19.2
GENERAL
FORMULAE
FOR
PREMIUMS
UNDER
DEDUCTIBLES
.
.
.
.
.
.
.
428
19.2.1
FRANCHISE
DEDUCTIBLE
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
429
19.2.2
FIXED
AMOUNT
DEDUCTIBLE
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
431
19.2.3
PROPORTIONAL
DEDUCTIBLE
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
432
19.2.4
LIMITED
PROPORTIONAL
DEDUCTIBLE
.
.
.
.
.
.
.
.
.
.
.
.
.
432
19.2.5
DISAPPEARING
DEDUCTIBLE
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
434
19.3
PREMIUMS
UNDER
DEDUCTIBLES
FOR
GIVEN
LOSS
DISTRIBUTIONS
.
.
.
436
19.3.1
LOG-NORMAL
LOSS
DISTRIBUTION
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
437
19.3.2
PARETO
LOSS
DISTRIBUTION
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
438
19.3.3
BURR
LOSS
DISTRIBUTION
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
441
19.3.4
WEIBULL
LOSS
DISTRIBUTION
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
445
19.3.5
GAMMA
LOSS
DISTRIBUTION
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
447
19.3.6
MIXTURE
OF
TWO
EXPONENTIALS
LOSS
DISTRIBUTION
.
.
.
.
.
449
19.4
FINAL
REMARKS
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
450
CONTENTS
11
20
PREMIUMS,
INVESTMENTS,
AND
REINSURANCE
453
PAWE L
MIYYSTA
AND
WOJCIECH
OTTO
20.1
INTRODUCTION
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
453
20.2
SINGLE-PERIOD
CRITERION
AND
THE
RATE
OF
RETURN
ON
CAPITAL
.
.
.
456
20.2.1
RISK
BASED
CAPITAL
CONCEPT
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
456
20.2.2
HOW
TO
CHOOSE
PARAMETER
VALUES?
.
.
.
.
.
.
.
.
.
.
.
.
457
20.3
THE
TOP-DOWN
APPROACH
TO
INDIVIDUAL
RISKS
PRICING
.
.
.
.
.
.
459
20.3.1
APPROXIMATIONS
OF
QUANTILES
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
459
20.3.2
MARGINAL
COST
BASIS
FOR
INDIVIDUAL
RISK
PRICING
.
.
.
.
.
460
20.3.3
BALANCING
PROBLEM
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
461
20.3.4
A
SOLUTION
FOR
THE
BALANCING
PROBLEM
.
.
.
.
.
.
.
.
.
.
462
20.3.5
APPLICATIONS
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
462
20.4
RATE
OF
RETURN
AND
REINSURANCE
UNDER
THE
SHORT
TERM
CRITERION
463
20.4.1
GENERAL
CONSIDERATIONS
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
464
20.4.2
ILLUSTRATIVE
EXAMPLE
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
465
20.4.3
INTERPRETATION
OF
NUMERICAL
CALCULATIONS
IN
EXAMPLE
2
.
467
20.5
RUIN
PROBABILITY
CRITERION
WHEN
THE
INITIAL
CAPITAL
IS
GIVEN
.
.
469
20.5.1
APPROXIMATION
BASED
ON
LUNDBERG
INEQUALITY
.
.
.
.
.
.
469
20.5.2
ZERO
APPROXIMATION
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
471
20.5.3
CRAMYYER{LUNDBERG
APPROXIMATION
.
.
.
.
.
.
.
.
.
.
.
.
471
20.5.4
BEEKMAN{BOWERS
APPROXIMATION
.
.
.
.
.
.
.
.
.
.
.
.
.
472
20.5.5
DIYYUSION
APPROXIMATION
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
473
20.5.6
DE
VYLDER
APPROXIMATION
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
474
20.5.7
SUBEXPONENTIAL
APPROXIMATION
.
.
.
.
.
.
.
.
.
.
.
.
.
.
475
20.5.8
PANJER
APPROXIMATION
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
475
20.6
RUIN
PROBABILITY
CRITERION
AND
THE
RATE
OF
RETURN
.
.
.
.
.
.
.
477
20.6.1
FIXED
DIVIDENDS
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
477
12
CONTENTS
20.6.2
FLEXIBLE
DIVIDENDS
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
479
20.7
RUIN
PROBABILITY,
RATE
OF
RETURN
AND
REINSURANCE
.
.
.
.
.
.
.
481
20.7.1
FIXED
DIVIDENDS
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
481
20.7.2
INTERPRETATION
OF
SOLUTIONS
OBTAINED
IN
EXAMPLE
5
.
.
.
482
20.7.3
FLEXIBLE
DIVIDENDS
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
484
20.7.4
INTERPRETATION
OF
SOLUTIONS
OBTAINED
IN
EXAMPLE
6
.
.
.
485
20.8
FINAL
REMARKS
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
487
III
GENERAL
489
21
WORKING
WITH
THE
XQC
491
SZYMON
BORAK,
WOLFGANG
HARDLE,
AND
HEIKO
LEHMANN
21.1
INTRODUCTION
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
491
21.2
THE
XPLORE
QUANTLET
CLIENT
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
492
21.2.1
CONYYGURATION
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
492
21.2.2
GETTING
CONNECTED
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
493
21.3
DESKTOP
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
494
21.3.1
XPLORE
QUANTLET
EDITOR
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
495
21.3.2
DATA
EDITOR
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
496
21.3.3
METHOD
TREE
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
501
21.3.4
GRAPHICAL
OUTPUT
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
503
INDEX
507
|
| any_adam_object | 1 |
| author2 | Čížek, Pavel |
| author2_role | edt |
| author2_variant | p č pč |
| author_GND | (DE-588)129834866 |
| author_facet | Čížek, Pavel |
| building | Verbundindex |
| bvnumber | BV019733945 |
| callnumber-first | H - Social Science |
| callnumber-label | HG173 |
| callnumber-raw | HG173 |
| callnumber-search | HG173 |
| callnumber-sort | HG 3173 |
| callnumber-subject | HG - Finance |
| classification_rvk | QH 230 SK 980 |
| ctrlnum | (OCoLC)224579413 (DE-599)BVBBV019733945 |
| dewey-full | 332'.015195 |
| dewey-hundreds | 300 - Social sciences |
| dewey-ones | 332 - Financial economics |
| dewey-raw | 332'.015195 |
| dewey-search | 332'.015195 |
| dewey-sort | 3332 515195 |
| dewey-tens | 330 - Economics |
| discipline | Mathematik Wirtschaftswissenschaften |
| edition | 1. Ed. |
| format | Book |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T20:04:53Z |
| institution | BVB |
| isbn | 3540221891 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-013060788 |
| oclc_num | 224579413 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-11 |
| owner_facet | DE-91G DE-BY-TUM DE-11 |
| physical | 400 S. 235 mm x 155 mm |
| publishDate | 2004 |
| publishDateSearch | 2004 |
| publishDateSort | 2004 |
| publisher | Springer |
| record_format | marc |
| spelling | Statistical tools in finance and insurance Hrsg. Pavel Cizek ... 1. Ed. Berlin Springer 2004 400 S. 235 mm x 155 mm txt rdacontent n rdamedia nc rdacarrier Assurance - Méthodes statistiques Finances - Méthodes statistiques Mathematik Mathematisches Modell Finance Mathematical models Insurance Mathematics Versicherungsmathematik (DE-588)4063194-1 gnd rswk-swf Finanzmathematik (DE-588)4017195-4 gnd rswk-swf Versicherungsmathematik (DE-588)4063194-1 s DE-604 Finanzmathematik (DE-588)4017195-4 s Čížek, Pavel (DE-588)129834866 edt DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013060788&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Statistical tools in finance and insurance Assurance - Méthodes statistiques Finances - Méthodes statistiques Mathematik Mathematisches Modell Finance Mathematical models Insurance Mathematics Versicherungsmathematik (DE-588)4063194-1 gnd Finanzmathematik (DE-588)4017195-4 gnd |
| subject_GND | (DE-588)4063194-1 (DE-588)4017195-4 |
| title | Statistical tools in finance and insurance |
| title_auth | Statistical tools in finance and insurance |
| title_exact_search | Statistical tools in finance and insurance |
| title_full | Statistical tools in finance and insurance Hrsg. Pavel Cizek ... |
| title_fullStr | Statistical tools in finance and insurance Hrsg. Pavel Cizek ... |
| title_full_unstemmed | Statistical tools in finance and insurance Hrsg. Pavel Cizek ... |
| title_short | Statistical tools in finance and insurance |
| title_sort | statistical tools in finance and insurance |
| topic | Assurance - Méthodes statistiques Finances - Méthodes statistiques Mathematik Mathematisches Modell Finance Mathematical models Insurance Mathematics Versicherungsmathematik (DE-588)4063194-1 gnd Finanzmathematik (DE-588)4017195-4 gnd |
| topic_facet | Assurance - Méthodes statistiques Finances - Méthodes statistiques Mathematik Mathematisches Modell Finance Mathematical models Insurance Mathematics Versicherungsmathematik Finanzmathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013060788&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT cizekpavel statisticaltoolsinfinanceandinsurance |