Semi-Markov risk models for finance, insurance and reliability:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York
Springer
2007
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | XVII, 429 S. graph. Darst. |
| ISBN: | 9780387707297 0387707298 0387707301 |
Internformat
MARC
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| 100 | 1 | |a Janssen, Jacques |d 1939- |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Semi-Markov risk models for finance, insurance and reliability |c by Jacques Janssen ; Raimondo Manca |
| 264 | 1 | |a New York |b Springer |c 2007 | |
| 300 | |a XVII, 429 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 7 | |a Financiering |2 gtt | |
| 650 | 7 | |a Markov-modellen |2 gtt | |
| 650 | 4 | |a Processus de Markov | |
| 650 | 7 | |a Risicoanalyse |2 gtt | |
| 650 | 4 | |a Risque (Assurance) - Modèles mathématiques | |
| 650 | 4 | |a Risque - Modèles mathématiques | |
| 650 | 4 | |a Risque financier - Modèles mathématiques | |
| 650 | 7 | |a Verzekeringen |2 gtt | |
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Financial risk |x Mathematical models | |
| 650 | 4 | |a Markov processes | |
| 650 | 4 | |a Risk (Insurance) |x Mathematical models | |
| 650 | 4 | |a Risk |x Mathematical models | |
| 650 | 0 | 7 | |a Risiko |0 (DE-588)4050129-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Semi-Markov-Modell |0 (DE-588)4180964-6 |2 gnd |9 rswk-swf |
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| 700 | 1 | |a Manca, Raimondo |e Verfasser |4 aut | |
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| 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=015688115&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |3 Klappentext |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-015688115 | ||
Datensatz im Suchindex
| _version_ | 1804136571848359937 |
|---|---|
| adam_text | Contents
Preface
XV
1
Probability Tools for Stochastic Modelling
1
1
The Sample Space
1
2
Probability Space
2
3
Random Variables
6
4
Integrability, Expectation and Independence
8
5
Main Distribution Probabilities
14
5.1
The Binomial Distribution
15
5.2
The
Poisson
Distribution
16
5.3
The Normal (or Laplace-Gauss) Distribution
16
5.4
The Log-Normal Distribution
19
5.5
The Negative Exponential Distribution
20
5.6
The Multidimensional Normal Distribution
20
6
Conditioning (From Independence to Dependence)
22
6.1
Conditioning: Introductory Case
22
6.2
Conditioning: General Case
26
6.3
Regular Conditional Probability
30
7
Stochastic Processes
34
8
Martingales
37
9
Brownian Motion
40
2
Renewal Theory and Markov Chains
43
1
Purpose of Renewal Theory
43
2
Main Definitions
44
3
Classification of Renewal Processes
45
4
The Renewal Equation
50
5
The Use of Laplace Transform
55
5.1
The Laplace Transform
55
5.2
The Laplace-Stieltjes (L-S) Transform
55
6
Application of Wald s Identity
56
7
Asymptotical Behaviour of the
7V(ţ)-Process
57
8
Delayed and Stationary Renewal Processes
57
9
Markov Chains
58
9.1
Definitions
58
9.2
Markov Chain State Classification
62
9.3
Occupation Times
66
9.4
Computations of Absorption Probabilities
67
9.5
Asymptotic Behaviour
67
VI
Contents
9.6
Examples
71
9.7
A Case Study in Social Insurance
(Janssen
(1966)) 74
3
Markov Renewal Processes, Semi-Markov Processes And
Markov Random Walks
77
1
Positive
(J
-Х)
Processes
77
2
Semi-Markov and Extended Semi-Markov Chains
78
3
Primary Properties
79
4
Examples
83
5
Markov Renewal Processes, Semi-Markov and
Associated Counting Processes
85
6
Markov Renewal Functions
87
7
Classification of the States of an MRP
90
8
The Markov Renewal Equation
91
9
Asymptotic Behaviour of an MRP
92
9.1
Asymptotic Behaviour of Markov Renewal Functions
92
9.2
Asymptotic Behaviour of Solutions of Markov Renewal
Equations
93
10
Asymptotic Behaviour of SMP
94
10.1
Irreducible Case
94
10.2
Non-irreducible Case
96
10.2.1
Uni-Reducible Case
96
10.2.2
General Case
97
11
Delayed and Stationary MRP
98
12
Particular Cases of MRP
102
12.1
Renewal Processes and Markov Chains
102
12.2
MRP of Zero Order (PYKE
(1962)) 102
12.2.1
First Type of Zero Order MRP
102
12.2.2
Second Type of Zero Order MRP
103
12.3
Continuous Markov Processes
104
13
A Case Study in Social Insurance
(Janssen
(1966)) 104
13.1
The Semi-Markov Model
104
13.2
Numerical Example
105
14
(J
-Х)
Processes
106
15
Functionals of
(J
-Х)
Processes
107
16
Functionals of Positive
(J
-Х)
Processes
111
17
Classical Random Walks and Risk Theory
112
17.1
Purpose
112
17.2
Basic Notions on Random Walks
112
17.3
Classification of Random Walks
115
18
Defective Positive
(J
-Х)
Processes
117
19
Semi-Markov Random Walks
121
Contents
VII
20 Distribution
of the Supremum for Semi-Markov
Random Walks
123
21
Non-
Homogeneous Markov and Semi-Markov Processes
124
21.1
General Definitions
124
21.1.1
Completely Non-Homogeneous Semi-Markov
Processes
124
21.1.2
Special Cases
128
4
Discrete Time and Reward SMP and their Numerical Treatment
131
1
Discrete Time Semi-Markov Processes
131
1.1
Purpose
131
1.2
DTSMP Definition
131
2
Numerical Treatment of SMP
133
3
DTSMP and SMP Numerical Solutions
13 7
4
Solution of DTHSMP and DTNHSMP in the Transient Case:
a Transportation Example
142
4.1.
Principle of the Solution
142
4.2.
Semi-Markov Transportation Example
143
4.2.1
Homogeneous Case
143
4.2.2
Non-Homogeneous Case
147
5
Continuous and Discrete Time Reward Processes
149
5.1
Classification and Notation
15 0
5.1.1
Classification of Reward Processes
150
5.1.2
Financial Parameters
151
5.2
Undiscounted SMRWP
153
5.2.1
Fixed Permanence Rewards
153
5.2.2
Variable Permanence and Transition Rewards
154
5.2.3
Non-Homogeneous Permanence and Transition
Rewards
155
5.3
Discounted SMRWP
156
5.3.1
Fixed Permanence and Interest Rate Cases
156
5.3.2
Variable Interest Rates, Permanence
and Transition Cases
158
5.3.3
Non-Homogeneous Interest Rate, Permanence
and Transition Case
159
6
General Algorithms for DTSMRWP
159
7
Numerical Treatment of SMRWP
161
7.1
Undiscounted Case
161
7.2
Discounted Case
163
8
Relation Between DTSMRWP and SMRWP Numerical
Solutions
165
8.1
Undiscounted Case
166
8.2
Discounted Case
168
VIII Contents
5
Semi-Markov Extensions of the Black-Scholes Model
171
1
Introduction to Option Theory
171
2
The Cox-Ross-Rubinstein (CRR) or Binomial Model
174
2.1
One-Period Model
175
2.1.1
The Arbitrage Model
176
2.1.2
Numerical Example
177
2.2
Multi-Period Model
178
2.2.1
Case of Two Periods
178
2.2.2
Case of
η
Periods
179
2.2.3
Numerical Example
180
3
The Black-Scholes Formula as Limit of the Binomial
Model
181
3.1
The Log-Normality of the Underlying Asset
181
3.2.
The Black-Scholes Formula
183
4
The Black-Scholes Continuous Time Model
184
4.1
The Model
184
4.2
The
Ito or
Stochastic Calculus
184
4.3
The Solution of the Black-Scholes-Samuelson
Model
186
4.4
Pricing the Call with the Black-Scholes-Samuelson
Model
188
4.4.1
The Hedging Portfolio
188
4.4.2
The Risk Neutral Measure and the Martingale
Property
190
4.4.3
The Call-Put Parity Relation
191
5
Exercise on Option Pricing
192
6
The Greek Parameters
193
6.1
Introduction
193
6.2
Values of the Greek Parameters
195
6.3
Exercises
196
7
The Impact of Dividend Distribution
198
8
Estimation of the Volatility
199
8.1
Historic Method
199
8.2
Implicit Volatility Method
200
9
Black and Scholes on the Market
201
9.1
Empirical Studies
201
9.2
Smile Effect
201
10
The
Janssen-Manca
Model
201
10.1
The Markov Extension of the One-Period
CRR Model
202
10.1.1
The Model
202
10.1.2
Computational Option Pricing Formula for the
One-Period Model
206
Contents
IX
10.1.3
Examples
207
10.2
The Multi-Period Discrete Markov Chain Model
209
10.3
The Multi-Period Discrete Markov Chain Limit
Model
211
10.4
The Extension of the Black-Scholes Pricing
Formula with Markov Environment:
The
Janssen-Manca
Formula
213
11
The Extension of the Black-Scholes Pricing Formula
with Markov Environment: The Semi-Markovian
Janssen-Manca-Volpe
formula
216
11.1
Introduction
216
11.2
The Janssen-Manca-Cinlar Model
216
11.2.1
The JMC
(Janssen-Manca-Çinlar)
Semi-
Markov Model
(1995, 1998) 217
11.2.2
The Explicit Expression of S(t)
218
11.3
Call Option Pricing
219
11.4
Stationary Option Pricing Formula
221
12
Markov and Semi-Markov Option Pricing Models with
Arbitrage Possibility
222
12.1
Introduction to the
Janssen-Manca-Di Biase
Models
222
12.2
The Homogeneous Markov JMD
(Janssen-Manca-
Di
Biase) Model for the Underlying Asset
223
12.3
Particular Cases
224
12.4
Numerical Example for the JMD Markov Model
225
12.5
The Continuous Time Homogeneous Semi-Markov
JMD Model for the Underlying Asset
227
12.6
Numerical Example for the Semi-Markov
JMD Model
228
12.7
Conclusion
229
6
Other Semi-Markov Models in Finance and Insurance
231
1
Exchange of Dated Sums in a Stochastic Homogeneous
Environment
231
1.1
Introduction
231
1.2
Deterministic Axiomatic Approach to Financial Choices
232
1.3
The Homogeneous Stochastic Approach
234
1.4
Continuous Time Models with Finite State Space
235
1.5
Discrete Time Model with Finite State Space
236
1.6
An Example of Asset Evaluation
237
1.7
Two Transient Case Examples
238
1.8
Financial Application of Asymptotic Results
244
2
Discrete Time Markov and Semi-Markov Reward Processes
and Generalised Annuities
245
X
Contents
2.1
Annuities and Markov Reward Processes
246
2.2
HSMRWP and Stochastic Annuities Generalization
248
3
Semi-Markov Model for Interest Rate Structure
251
3.1
The Deterministic Environment
251
3.2
The Homogeneous Stochastic Interest Rate Approach
252
3.3
Discount Factors
253
3.4
An Applied Example in the Homogeneous Case
255
3.5
A Factor Discount Example in the Non-Homogeneous
Case
257
4
Future Pricing Model
259
4.1
Description of Data
260
4.2
The Input Model
261
4.3
The Results
262
5
A Social Security Application with Real Data
265
5.1
The Transient Case Study
265
5.2
The Asymptotic Case
267
6
Semi-Markov Reward Multiple-Life Insurance Models
269
7
Insurance Model with Stochastic Interest Rates
276
7.1
Introduction
276
7.2
The Actuarial Problem
276
7.3
A Semi-Markov Reward Stochastic Interest Rate Model
277
7
Insurance Risk Models
281
1
Classical Stochastic Models for Risk Theory and Ruin
Probability
281
1.1
The G/G or E.S. Andersen Risk Model
282
.1.1
The Model
282
.1.2
The Premium
282
. 1.3
Three Basic Processes
284
1.1.4
The Ruin Problem
285
1.2
The P/G or Cramer-Lundberg Risk Model
287
1.2.1
The Model
287
1.2.2
The Ruin Probability
288
1.2.3
Risk Management Using Ruin Probability
293
1.2.4
Cramer s Estimator
294
2
Diffusion Models for Risk Theory and Ruin Probability
301
2.1
The Simple Diffusion Risk Model
301
2.2
The ALM-Like Risk Model
(Janssen
(1991), (1993))
302
2.3
Comparison of ALM-Like and Cramer-Lundberg Risk
Models
304
2.4
The Second ALM-Like Risk Model
305
3
Semi-Markov Risk Models
309
Contents
XI
3
.1
The Semi-Markov Risk Model (or SMRM)
309
3.1.1
The General SMR Model
309
3.1.2
The Counting Claim Process
312
3.1.3
The Accumulated Claim Amount Process
314
3.1.4
The Premium Process
315
3.1.5
The Risk and Risk Reserve Processes
316
3.2
The Stationary Semi-Markov Risk Model
316
3.3
Particular SMRM with Conditional
Independence
316
3.3.1
The SM/G Model
317
3.3.2
The G/SM Model
317
3.3.3
The P/SM Model
317
3.3.4
The M/SM Model
318
3.3.5
The
M
7SM Model
318
3.3.6
The SM(0)/SM(0) Model
318
3.3.7
The SM (0)/SM (0) Model
318
3.3.8
The Mixed Zero Order SM
(OySMCO) and
SM(0)/SM!
(0)
Models
319
3.4
The Ruin Problem for the General SMRM
320
3.4.1
Ruin and Non-Ruin Probabilities
320
3.4.2
Change of Premium Rate
321
3.4.3
General Solution of the Asymptotic Ruin
Probability Problem for a General SMRM
322
3.5
The Ruin Problem for Particular SMRM
324
3.5.1
The Zero Order Model
ЅМСОуЅМф)
324
3.5.2
The Zero Order Model SM (0)/SM
(0) 325
3.5.3
The Model M/SM
325
3.5.4
The Zero Order Models as Special Case
of the Model M/SM
328
3.6
The
M VSM
Model
329
3.6.1
General Solution
329
3.6.2
Particular Cases: the M/M and
M /M
Models
332
8
Reliability and Credit Risk Models
335
1
Classical Reliability Theory
335
1.1
Basic Concepts
335
1.2
Classification of Failure Rates
336
1.3
Main Distributions Used in Reliability
338
1.4
Basic Indicators of Reliability
339
1.5
Complex and Coherent Structures
340
2
Stochastic Modelling in Reliability Theory
343
2.1
Maintenance Systems
343
2.2
The Semi-Markov Model for Maintenance Systems
346
2.3
A Classical Example
348
XII Contents
3
Stochastic Modelling for Credit Risk Management
351
3.1
The Problem of Credit Risk
351
3.2
Construction of a Rating Using the Merton Model
for the Firm
352
3.3
Time Dynamic Evolution of a Rating
355
3.3.1
Time Continuous Model
355
3.3.2
Discrete Continuous Model
356
3.3.3
Example
358
3.3.4
Rating and Spreads on Zero Bonds
360
4
Credit Risk as a Reliability Model
361
4.1
The Semi-Markov Reliability Credit Risk Model
361
4.2
A Homogeneous Case Example
362
4.3
A Non-Homogeneous Case Example
365
9
Generalised Non-Homogeneous Models for Pension Funds and
Manpower Management
373
1
Application to Pension Funds Evolution
373
1.1
Introduction
374
1.2
The Non-homogeneous Semi-Markov Pension Fund
Model
375
1.2.1
The DTNHSM Model
376
1.2.2
The States of DTNHSMPFM
379
1.2.3
The Concept of Seniority in the DTNHSPFM
379
1.3
The Reserve Structure
382
1.4
The Impact of Inflation and Interest Variability
383
1.5
Solving Evolution Equations
385
1.6
The Dynamic Population Evolution of the Pension
Funds
389
1.7
Financial Equilibrium of the Pension Funds
392
1.8
Scenario and Data
395
1.8.1
Internal Scenario
396
1.8.2
Historical Data
396
1.8.3
Economic Scenario
397
1.9
Usefulness of the NHSMPFM
398
2
Generalized Non-Homogeneous Semi-Markov Model for
Manpower Management
399
2.1
Introduction
399
2.2
GDTNHSMP for the Evolution of Salary Lines
400
2.3
The GDTNHSMRWP for Reserve Structure
402
2.4
Reserve Structure Stochastic Interest Rate
403
2.5
The Dynamics of Population Evolution
404
2.6
The Computation of Salary Cost Present Value
405
Contents
References
407
Author index
423
Subject index
425
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Contents
Preface
XV
1
Probability Tools for Stochastic Modelling
1
1
The Sample Space
1
2
Probability Space
2
3
Random Variables
6
4
Integrability, Expectation and Independence
8
5
Main Distribution Probabilities
14
5.1
The Binomial Distribution
15
5.2
The
Poisson
Distribution
16
5.3
The Normal (or Laplace-Gauss) Distribution
16
5.4
The Log-Normal Distribution
19
5.5
The Negative Exponential Distribution
20
5.6
The Multidimensional Normal Distribution
20
6
Conditioning (From Independence to Dependence)
22
6.1
Conditioning: Introductory Case
22
6.2
Conditioning: General Case
26
6.3
Regular Conditional Probability
30
7
Stochastic Processes
34
8
Martingales
37
9
Brownian Motion
40
2
Renewal Theory and Markov Chains
43
1
Purpose of Renewal Theory
43
2
Main Definitions
44
3
Classification of Renewal Processes
45
4
The Renewal Equation
50
5
The Use of Laplace Transform
55
5.1
The Laplace Transform
55
5.2
The Laplace-Stieltjes (L-S) Transform
55
6
Application of Wald's Identity
56
7
Asymptotical Behaviour of the
7V(ţ)-Process
57
8
Delayed and Stationary Renewal Processes
57
9
Markov Chains
58
9.1
Definitions
58
9.2
Markov Chain State Classification
62
9.3
Occupation Times
66
9.4
Computations of Absorption Probabilities
67
9.5
Asymptotic Behaviour
67
VI
Contents
9.6
Examples
71
9.7
A Case Study in Social Insurance
(Janssen
(1966)) 74
3
Markov Renewal Processes, Semi-Markov Processes And
Markov Random Walks
77
1
Positive
(J
-Х)
Processes
77
2
Semi-Markov and Extended Semi-Markov Chains
78
3
Primary Properties
79
4
Examples
83
5
Markov Renewal Processes, Semi-Markov and
Associated Counting Processes
85
6
Markov Renewal Functions
87
7
Classification of the States of an MRP
90
8
The Markov Renewal Equation
91
9
Asymptotic Behaviour of an MRP
92
9.1
Asymptotic Behaviour of Markov Renewal Functions
92
9.2
Asymptotic Behaviour of Solutions of Markov Renewal
Equations
93
10
Asymptotic Behaviour of SMP
94
10.1
Irreducible Case
94
10.2
Non-irreducible Case
96
10.2.1
Uni-Reducible Case
96
10.2.2
General Case
97
11
Delayed and Stationary MRP
98
12
Particular Cases of MRP
102
12.1
Renewal Processes and Markov Chains
102
12.2
MRP of Zero Order (PYKE
(1962)) 102
12.2.1
First Type of Zero Order MRP
102
12.2.2
Second Type of Zero Order MRP
103
12.3
Continuous Markov Processes
104
13
A Case Study in Social Insurance
(Janssen
(1966)) 104
13.1
The Semi-Markov Model
104
13.2
Numerical Example
105
14
(J
-Х)
Processes
106
15
Functionals of
(J
-Х)
Processes
107
16
Functionals of Positive
(J
-Х)
Processes
111
17
Classical Random Walks and Risk Theory
112
17.1
Purpose
112
17.2
Basic Notions on Random Walks
112
17.3
Classification of Random Walks
115
18
Defective Positive
(J
-Х)
Processes
117
19
Semi-Markov Random Walks
121
Contents
VII
20 Distribution
of the Supremum for Semi-Markov
Random Walks
123
21
Non-
Homogeneous Markov and Semi-Markov Processes
124
21.1
General Definitions
124
21.1.1
Completely Non-Homogeneous Semi-Markov
Processes
124
21.1.2
Special Cases
128
4
Discrete Time and Reward SMP and their Numerical Treatment
131
1
Discrete Time Semi-Markov Processes
131
1.1
Purpose
131
1.2
DTSMP Definition
131
2
Numerical Treatment of SMP
133
3
DTSMP and SMP Numerical Solutions
13 7
4
Solution of DTHSMP and DTNHSMP in the Transient Case:
a Transportation Example
142
4.1.
Principle of the Solution
142
4.2.
Semi-Markov Transportation Example
143
4.2.1
Homogeneous Case
143
4.2.2
Non-Homogeneous Case
147
5
Continuous and Discrete Time Reward Processes
149
5.1
Classification and Notation
15 0
5.1.1
Classification of Reward Processes
150
5.1.2
Financial Parameters
151
5.2
Undiscounted SMRWP
153
5.2.1
Fixed Permanence Rewards
153
5.2.2
Variable Permanence and Transition Rewards
154
5.2.3
Non-Homogeneous Permanence and Transition
Rewards
155
5.3
Discounted SMRWP
156
5.3.1
Fixed Permanence and Interest Rate Cases
156
5.3.2
Variable Interest Rates, Permanence
and Transition Cases
158
5.3.3
Non-Homogeneous Interest Rate, Permanence
and Transition Case
159
6
General Algorithms for DTSMRWP
159
7
Numerical Treatment of SMRWP
161
7.1
Undiscounted Case
161
7.2
Discounted Case
163
8
Relation Between DTSMRWP and SMRWP Numerical
Solutions
165
8.1
Undiscounted Case
166
8.2
Discounted Case
168
VIII Contents
5
Semi-Markov Extensions of the Black-Scholes Model
171
1
Introduction to Option Theory
171
2
The Cox-Ross-Rubinstein (CRR) or Binomial Model
174
2.1
One-Period Model
175
2.1.1
The Arbitrage Model
176
2.1.2
Numerical Example
177
2.2
Multi-Period Model
178
2.2.1
Case of Two Periods
178
2.2.2
Case of
η
Periods
179
2.2.3
Numerical Example
180
3
The Black-Scholes Formula as Limit of the Binomial
Model
181
3.1
The Log-Normality of the Underlying Asset
181
3.2.
The Black-Scholes Formula
183
4
The Black-Scholes Continuous Time Model
184
4.1
The Model
184
4.2
The
Ito or
Stochastic Calculus
184
4.3
The Solution of the Black-Scholes-Samuelson
Model
186
4.4
Pricing the Call with the Black-Scholes-Samuelson
Model
188
4.4.1
The Hedging Portfolio
188
4.4.2
The Risk Neutral Measure and the Martingale
Property
190
4.4.3
The Call-Put Parity Relation
191
5
Exercise on Option Pricing
192
6
The Greek Parameters
193
6.1
Introduction
193
6.2
Values of the Greek Parameters
195
6.3
Exercises
196
7
The Impact of Dividend Distribution
198
8
Estimation of the Volatility
199
8.1
Historic Method
199
8.2
Implicit Volatility Method
200
9
Black and Scholes on the Market
201
9.1
Empirical Studies
201
9.2
Smile Effect
201
10
The
Janssen-Manca
Model
201
10.1
The Markov Extension of the One-Period
CRR Model
202
10.1.1
The Model
202
10.1.2
Computational Option Pricing Formula for the
One-Period Model
206
Contents
IX
10.1.3
Examples
207
10.2
The Multi-Period Discrete Markov Chain Model
209
10.3
The Multi-Period Discrete Markov Chain Limit
Model
211
10.4
The Extension of the Black-Scholes Pricing
Formula with Markov Environment:
The
Janssen-Manca
Formula
213
11
The Extension of the Black-Scholes Pricing Formula
with Markov Environment: The Semi-Markovian
Janssen-Manca-Volpe
formula
216
11.1
Introduction
216
11.2
The Janssen-Manca-Cinlar Model
216
11.2.1
The JMC
(Janssen-Manca-Çinlar)
Semi-
Markov Model
(1995, 1998) 217
11.2.2
The Explicit Expression of S(t)
218
11.3
Call Option Pricing
219
11.4
Stationary Option Pricing Formula
221
12
Markov and Semi-Markov Option Pricing Models with
Arbitrage Possibility
222
12.1
Introduction to the
Janssen-Manca-Di Biase
Models
222
12.2
The Homogeneous Markov JMD
(Janssen-Manca-
Di
Biase) Model for the Underlying Asset
223
12.3
Particular Cases
224
12.4
Numerical Example for the JMD Markov Model
225
12.5
The Continuous Time Homogeneous Semi-Markov
JMD Model for the Underlying Asset
227
12.6
Numerical Example for the Semi-Markov
JMD Model
228
12.7
Conclusion
229
6
Other Semi-Markov Models in Finance and Insurance
231
1
Exchange of Dated Sums in a Stochastic Homogeneous
Environment
231
1.1
Introduction
231
1.2
Deterministic Axiomatic Approach to Financial Choices
232
1.3
The Homogeneous Stochastic Approach
234
1.4
Continuous Time Models with Finite State Space
235
1.5
Discrete Time Model with Finite State Space
236
1.6
An Example of Asset Evaluation
237
1.7
Two Transient Case Examples
238
1.8
Financial Application of Asymptotic Results
244
2
Discrete Time Markov and Semi-Markov Reward Processes
and Generalised Annuities
245
X
Contents
2.1
Annuities and Markov Reward Processes
246
2.2
HSMRWP and Stochastic Annuities Generalization
248
3
Semi-Markov Model for Interest Rate Structure
251
3.1
The Deterministic Environment
251
3.2
The Homogeneous Stochastic Interest Rate Approach
252
3.3
Discount Factors
253
3.4
An Applied Example in the Homogeneous Case
255
3.5
A Factor Discount Example in the Non-Homogeneous
Case
257
4
Future Pricing Model
259
4.1
Description of Data
260
4.2
The Input Model
261
4.3
The Results
262
5
A Social Security Application with Real Data
265
5.1
The Transient Case Study
265
5.2
The Asymptotic Case
267
6
Semi-Markov Reward Multiple-Life Insurance Models
269
7
Insurance Model with Stochastic Interest Rates
276
7.1
Introduction
276
7.2
The Actuarial Problem
276
7.3
A Semi-Markov Reward Stochastic Interest Rate Model
277
7
Insurance Risk Models
281
1
Classical Stochastic Models for Risk Theory and Ruin
Probability
281
1.1
The G/G or E.S. Andersen Risk Model
282
.1.1
The Model
282
.1.2
The Premium
282
. 1.3
Three Basic Processes
284
1.1.4
The Ruin Problem
285
1.2
The P/G or Cramer-Lundberg Risk Model
287
1.2.1
The Model
287
1.2.2
The Ruin Probability
288
1.2.3
Risk Management Using Ruin Probability
293
1.2.4
Cramer's Estimator
294
2
Diffusion Models for Risk Theory and Ruin Probability
301
2.1
The Simple Diffusion Risk Model
301
2.2
The ALM-Like Risk Model
(Janssen
(1991), (1993))
302
2.3
Comparison of ALM-Like and Cramer-Lundberg Risk
Models
304
2.4
The Second ALM-Like Risk Model
305
3
Semi-Markov Risk Models
309
Contents
XI
3
.1
The Semi-Markov Risk Model (or SMRM)
309
3.1.1
The General SMR Model
309
3.1.2
The Counting Claim Process
312
3.1.3
The Accumulated Claim Amount Process
314
3.1.4
The Premium Process
315
3.1.5
The Risk and Risk Reserve Processes
316
3.2
The Stationary Semi-Markov Risk Model
316
3.3
Particular SMRM with Conditional
Independence
316
3.3.1
The SM/G Model
317
3.3.2
The G/SM Model
317
3.3.3
The P/SM Model
317
3.3.4
The M/SM Model
318
3.3.5
The
M
7SM Model
318
3.3.6
The SM(0)/SM(0) Model
318
3.3.7
The SM'(0)/SM'(0) Model
318
3.3.8
The Mixed Zero Order SM
'
(OySMCO) and
SM(0)/SM!
(0)
Models
319
3.4
The Ruin Problem for the General SMRM
320
3.4.1
Ruin and Non-Ruin Probabilities
320
3.4.2
Change of Premium Rate
321
3.4.3
General Solution of the Asymptotic Ruin
Probability Problem for a General SMRM
322
3.5
The Ruin Problem for Particular SMRM
324
3.5.1
The Zero Order Model
ЅМСОуЅМф)
324
3.5.2
The Zero Order Model SM '(0)/SM
'(0) 325
3.5.3
The Model M/SM
325
3.5.4
The Zero Order Models as Special Case
of the Model M/SM
328
3.6
The
M VSM
Model
329
3.6.1
General Solution
329
3.6.2
Particular Cases: the M/M and
M '/M
Models
332
8
Reliability and Credit Risk Models
335
1
Classical Reliability Theory
335
1.1
Basic Concepts
335
1.2
Classification of Failure Rates
336
1.3
Main Distributions Used in Reliability
338
1.4
Basic Indicators of Reliability
339
1.5
Complex and Coherent Structures
340
2
Stochastic Modelling in Reliability Theory
343
2.1
Maintenance Systems
343
2.2
The Semi-Markov Model for Maintenance Systems
346
2.3
A Classical Example
348
XII Contents
3
Stochastic Modelling for Credit Risk Management
351
3.1
The Problem of Credit Risk
351
3.2
Construction of a Rating Using the Merton Model
for the Firm
352
3.3
Time Dynamic Evolution of a Rating
355
3.3.1
Time Continuous Model
355
3.3.2
Discrete Continuous Model
356
3.3.3
Example
358
3.3.4
Rating and Spreads on Zero Bonds
360
4
Credit Risk as a Reliability Model
361
4.1
The Semi-Markov Reliability Credit Risk Model
361
4.2
A Homogeneous Case Example
362
4.3
A Non-Homogeneous Case Example
365
9
Generalised Non-Homogeneous Models for Pension Funds and
Manpower Management
373
1
Application to Pension Funds Evolution
373
1.1
Introduction
374
1.2
The Non-homogeneous Semi-Markov Pension Fund
Model
375
1.2.1
The DTNHSM Model
376
1.2.2
The States of DTNHSMPFM
379
1.2.3
The Concept of Seniority in the DTNHSPFM
379
1.3
The Reserve Structure
382
1.4
The Impact of Inflation and Interest Variability
383
1.5
Solving Evolution Equations
385
1.6
The Dynamic Population Evolution of the Pension
Funds
389
1.7
Financial Equilibrium of the Pension Funds
392
1.8
Scenario and Data
395
1.8.1
Internal Scenario
396
1.8.2
Historical Data
396
1.8.3
Economic Scenario
397
1.9
Usefulness of the NHSMPFM
398
2
Generalized Non-Homogeneous Semi-Markov Model for
Manpower Management
399
2.1
Introduction
399
2.2
GDTNHSMP for the Evolution of Salary Lines
400
2.3
The GDTNHSMRWP for Reserve Structure
402
2.4
Reserve Structure Stochastic Interest Rate
403
2.5
The Dynamics of Population Evolution
404
2.6
The Computation of Salary Cost Present Value
405
Contents
References
407
Author index
423
Subject index
425
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| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Janssen, Jacques 1939- Manca, Raimondo |
| author_facet | Janssen, Jacques 1939- Manca, Raimondo |
| author_role | aut aut |
| author_sort | Janssen, Jacques 1939- |
| author_variant | j j jj r m rm |
| building | Verbundindex |
| bvnumber | BV022480762 |
| callnumber-first | H - Social Science |
| callnumber-label | HD61 |
| callnumber-raw | HD61 |
| callnumber-search | HD61 |
| callnumber-sort | HD 261 |
| callnumber-subject | HD - Industries, Land Use, Labor |
| classification_rvk | QH 237 SK 820 SK 980 |
| ctrlnum | (OCoLC)141384136 (DE-599)BVBBV022480762 |
| dewey-full | 332.01/519233 658.15501519233 |
| dewey-hundreds | 300 - Social sciences 600 - Technology (Applied sciences) |
| dewey-ones | 332 - Financial economics 658 - General management |
| dewey-raw | 332.01/519233 658.15501519233 |
| dewey-search | 332.01/519233 658.15501519233 |
| dewey-sort | 3332.01 6519233 |
| dewey-tens | 330 - Economics 650 - Management and auxiliary services |
| discipline | Mathematik Wirtschaftswissenschaften |
| discipline_str_mv | Mathematik Wirtschaftswissenschaften |
| format | Book |
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| id | DE-604.BV022480762 |
| illustrated | Illustrated |
| index_date | 2024-07-02T17:48:10Z |
| indexdate | 2024-07-09T20:58:31Z |
| institution | BVB |
| isbn | 9780387707297 0387707298 0387707301 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015688115 |
| oclc_num | 141384136 |
| open_access_boolean | |
| owner | DE-824 DE-N2 DE-355 DE-BY-UBR DE-945 DE-703 DE-11 |
| owner_facet | DE-824 DE-N2 DE-355 DE-BY-UBR DE-945 DE-703 DE-11 |
| physical | XVII, 429 S. graph. Darst. |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Springer |
| record_format | marc |
| spelling | Janssen, Jacques 1939- Verfasser aut Semi-Markov risk models for finance, insurance and reliability by Jacques Janssen ; Raimondo Manca New York Springer 2007 XVII, 429 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Financiering gtt Markov-modellen gtt Processus de Markov Risicoanalyse gtt Risque (Assurance) - Modèles mathématiques Risque - Modèles mathématiques Risque financier - Modèles mathématiques Verzekeringen gtt Mathematisches Modell Financial risk Mathematical models Markov processes Risk (Insurance) Mathematical models Risk Mathematical models Risiko (DE-588)4050129-2 gnd rswk-swf Semi-Markov-Modell (DE-588)4180964-6 gnd rswk-swf Versicherung (DE-588)4063173-4 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Finanzwirtschaft (DE-588)4017214-4 gnd rswk-swf Finanzmathematik (DE-588)4017195-4 gnd rswk-swf Semi-Markov-Modell (DE-588)4180964-6 s Finanzwirtschaft (DE-588)4017214-4 s Versicherung (DE-588)4063173-4 s Mathematisches Modell (DE-588)4114528-8 s Risiko (DE-588)4050129-2 s Finanzmathematik (DE-588)4017195-4 s b DE-604 Manca, Raimondo Verfasser aut Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015688115&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015688115&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Janssen, Jacques 1939- Manca, Raimondo Semi-Markov risk models for finance, insurance and reliability Financiering gtt Markov-modellen gtt Processus de Markov Risicoanalyse gtt Risque (Assurance) - Modèles mathématiques Risque - Modèles mathématiques Risque financier - Modèles mathématiques Verzekeringen gtt Mathematisches Modell Financial risk Mathematical models Markov processes Risk (Insurance) Mathematical models Risk Mathematical models Risiko (DE-588)4050129-2 gnd Semi-Markov-Modell (DE-588)4180964-6 gnd Versicherung (DE-588)4063173-4 gnd Mathematisches Modell (DE-588)4114528-8 gnd Finanzwirtschaft (DE-588)4017214-4 gnd Finanzmathematik (DE-588)4017195-4 gnd |
| subject_GND | (DE-588)4050129-2 (DE-588)4180964-6 (DE-588)4063173-4 (DE-588)4114528-8 (DE-588)4017214-4 (DE-588)4017195-4 |
| title | Semi-Markov risk models for finance, insurance and reliability |
| title_auth | Semi-Markov risk models for finance, insurance and reliability |
| title_exact_search | Semi-Markov risk models for finance, insurance and reliability |
| title_exact_search_txtP | Semi-Markov risk models for finance, insurance and reliability |
| title_full | Semi-Markov risk models for finance, insurance and reliability by Jacques Janssen ; Raimondo Manca |
| title_fullStr | Semi-Markov risk models for finance, insurance and reliability by Jacques Janssen ; Raimondo Manca |
| title_full_unstemmed | Semi-Markov risk models for finance, insurance and reliability by Jacques Janssen ; Raimondo Manca |
| title_short | Semi-Markov risk models for finance, insurance and reliability |
| title_sort | semi markov risk models for finance insurance and reliability |
| topic | Financiering gtt Markov-modellen gtt Processus de Markov Risicoanalyse gtt Risque (Assurance) - Modèles mathématiques Risque - Modèles mathématiques Risque financier - Modèles mathématiques Verzekeringen gtt Mathematisches Modell Financial risk Mathematical models Markov processes Risk (Insurance) Mathematical models Risk Mathematical models Risiko (DE-588)4050129-2 gnd Semi-Markov-Modell (DE-588)4180964-6 gnd Versicherung (DE-588)4063173-4 gnd Mathematisches Modell (DE-588)4114528-8 gnd Finanzwirtschaft (DE-588)4017214-4 gnd Finanzmathematik (DE-588)4017195-4 gnd |
| topic_facet | Financiering Markov-modellen Processus de Markov Risicoanalyse Risque (Assurance) - Modèles mathématiques Risque - Modèles mathématiques Risque financier - Modèles mathématiques Verzekeringen Mathematisches Modell Financial risk Mathematical models Markov processes Risk (Insurance) Mathematical models Risk Mathematical models Risiko Semi-Markov-Modell Versicherung Finanzwirtschaft Finanzmathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015688115&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015688115&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
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