Mathematical finance: deterministic and stochastic models
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| Format: | Book |
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| Language: | English |
| Published: |
London
ISTE [u.a.]
2009
|
| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 831 - 837 |
| Physical Description: | XX, 852 S. graph. Darst. |
| ISBN: | 9781848210813 1848210817 |
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| 245 | 1 | 0 | |a Mathematical finance |b deterministic and stochastic models |c Jacques Janssen ; Raimondo Manca ; Ernesto Volpe di Prignano |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a London |b ISTE [u.a.] |c 2009 | |
| 300 | |a XX, 852 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Literaturverz. S. 831 - 837 | ||
| 650 | 4 | |a Finances - Modèles mathématiques | |
| 650 | 7 | |a Finances - Modèles mathématiques |2 ram | |
| 650 | 7 | |a Finanzmathematik |2 stw | |
| 650 | 4 | |a Investissements - Mathématiques | |
| 650 | 7 | |a Investissements - Mathématiques |2 ram | |
| 650 | 4 | |a Processus stochastiques | |
| 650 | 7 | |a Processus stochastiques |2 ram | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Finance |x Mathematical models | |
| 650 | 4 | |a Stochastic processes | |
| 650 | 4 | |a Investments |x Mathematics | |
| 650 | 0 | 7 | |a Finanzmathematik |0 (DE-588)4017195-4 |2 gnd |9 rswk-swf |
| 655 | 7 | |0 (DE-588)4006432-3 |a Bibliografie |2 gnd-content | |
| 655 | 7 | |0 (DE-588)4123623-3 |a Lehrbuch |2 gnd-content | |
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| 700 | 1 | |a Janssen, Jacques |d 1939- |e Sonstige |0 (DE-588)136691331 |4 oth | |
| 700 | 1 | |a Manca, Raimondo |e Sonstige |0 (DE-588)136691420 |4 oth | |
| 700 | 1 | |a Volpe di Prignano, Ernesto |e Sonstige |4 oth | |
| 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=017102809&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
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| adam_text | Table
of
Contents
Preface
............................................xvii
Part
I. Deterministic Models
............................... 1
Chapter
1.
Introductory Elements to Financial Mathematics
........... 3
1.1.
The object of traditional financial mathematics
................ 3
1.2.
Financial supplies. Preference and indifference relations
........... 4
1.2.1.
The subjective aspect of preferences
.................... 4
1.2.2.
Objective aspects of financial laws. The equivalence principle
... 10
1.3.
The dimensional viewpoint of financial quantities
.............. 11
Chapter
2.
Theory of Financial Laws
......................... 13
2.1.
Indifference relations and exchange laws for simple financial operations
13
2.2.
Two variable laws and exchange factors
.................... 17
2.3.
Derived quantities in the accumulation and discount laws
......... 19
2.3.1.
Accumulation
................................. 19
2.3.2.
Discounting
.................................. 22
2.4.
Decomposable financial lawas
......................... 24
2.4.1.
Weak and strong decomposability properties:
equivalence relations
................................ 24
2.4.2.
Equivalence classes: characteristic properties of
decomposable laws
................................. 27
2.5.
Uniform financial laws: mean evaluations
................... 32
2.5.1.
Theory of uniform exchange laws
..................... 32
2.5.2.
An outline of associative averages
.................... 35
2.5.3.
Average duration and average maturity
................. 37
2.5.4.
Average index of return: average rate
.................. 38
2.6.
Uniform decomposable financial laws: exponential regime
........ 39
vi
Mathematical Finance
Chapter
3.
Uniform Regimes in Financial Practice
................ 41
3.1.
Preliminary comments
.............................. 41
3.1.1.
Equivalent rates and intensities
...................... 42
3.2.
The regime of simple delayed interest
(SDI)
................. 42
3.3.
The regime of rational discount (RD)
..................... 45
3.4.
The regime of simple discount (SD)
...................... 48
3.5.
The regime of simple advance interest
(SAI)
................ 50
3.6.
Comments on the
SDI,
RD,
SD
and
SAI
uniform regimes
......... 52
3.6.1.
Exchange factors (EF)
............................ 52
3.6.2.
Corrective operations
............................ 53
3.6.3.
Initial averaged intensities and instantaneous intensity
........ 53
3.6.4.
Average length in the linear law and their conjugates
......... 54
3.6.5.
Average rates in linear law and their conjugated laws
......... 54
3.7.
The compound interest regime
......................... 55
3.7.1.
Conversion of interests
........................... 55
3.7.2.
The regime of discretely compound interest
(DCI)
........... 56
3.7.3.
The regime of continuously compound interest
(CCI)
......... 63
3.8.
The regime of continuously comound discount
(CCD)
........... 69
3.9.
Complements and exercises on compound regimes
............. 74
3.10.
Comparison of laws of different regimes
................... 83
Chapter
4.
Financial Operations and their Evaluation:
Decisional Criteria
..................................... 91
4.1.
Calculation of capital values: fairness
..................... 91
4.2.
Retrospective and prospective reserve
..................... 97
4.3.
Usufruct and bare ownership in discrete and continuous cases
.... 104
4.4.
Methods and models for financial decisions and choices
.......... 107
4.4.1.
Internal rate as return index
........................ 107
4.4.2.
Outline on GDCF and internal financial law
............. 109
4.4.3.
Classifications and
propert
of financial projects
............
Ill
4.4.4.
Decisional criteria for financial projects
................. 114
4.4.5.
Choice criteria for mutually exclusive financial projects
....... 124
4.4.6.
Mixed projects: the TRM method
..................... 127
4.4.7.
Dicisional criteria on mixed projects
................... 133
4.5.
Appendix: outline on numberical methods for the solution of equations.
138
4.5.1.
General aspects
................................ 138
4.5.2.
The linear interpolation method
...................... 139
4.5.3.
Dichotomic method (or for successive divisions)
........... 141
4.5.4.
Secants and tangents method
........................ 142
4.5.5.
Classical alteration method
......................... 143
Table
of
Contents
vii
Chapter
5.
Annuities-Certain and their Value at Fixed Rate
..........147
5.1.
General aspects
...................................147
5.2.
Evaluation of constant installment annuities in the compound regime
. . 150
5.2.1.
Temporary annual annuity
......................... 150
5.2.2.
Annual perpetuity
.............................. 155
5.2.3.
Fractional and pluriannual annuities
................... 156
5.2.4.
Inequalities between annuity values with different frequency:
correction factors
.................................. 166
5.3.
Evaluation of constant installment annuities according to linear laws
. . 172
5.3.1.
The direct problem
.............................. 172
5.3.2.
Use of correction factors
.......................... 174
5.3.3.
Inverse problem
............................... 175
5.4.
Evaluation of varying installment annuities in the compound regime
. . 176
5.4.1.
General case
.................................176
5.4.2.
Specific cases: annual annuities in arithmetic progression
......179
5.4.3.
Specific cases: fractional and pluriannual annuities in
arithmetic progression
...............................183
5.4.4.
Specific cases: annual annuity in geometric progression
.......190
5.4.5.
Specific cases: fractional and pluriannual annuity in
geometric progression
...............................196
5.5.
Evaluation of varying installment annuities according to linear laws.
. . 204
5.5.1.
General case
.................................204
5.5.2.
Specific cases: annuities in arithmetic progression
...........205
5.5.3.
Specific cases: annuities in geometric progression
...........207
Chapter
6.
Loan Amortization and Funding Methods
..............211
6.1.
General features of loan amortization
.....................211
6.2.
General loan amortization at fixed rate
....................213
6.2.1.
Gradual
amortizatul
with varying installments
.............213
6.2.2.
Particular case: delayed constant installment amortization
......221
6.2.3.
Particular case: amortization with constant principal repayments
. . 225
6.2.4.
Particular case: amortization with advance interests
..........226
6.2.5.
Particular case: American amortization
................228
6.2.6.
Amortization in the continuous scheme
.................232
6.3.
Life amortization
.................................234
6.3.1.
Periodic advance payments
......................... 234
6.3.2.
Periodic payments with delayed principal amounts
.......... 241
6.3.3.
Continuous payment flow
......................... 242
6.4.
Periodic funcing at fixed rate
.......................... 244
6.4.1.
Delayed payments
..............................244
6.4.2.
Advance payments
..............................248
6.4.3.
Continuours payments
...........................251
viii
Mathematical Finance
6.5.
Amortizations with adjustment of rates and values
.............253
6.5.1.
Amortizations with adjustable rate
....................253
6.5.2.
Amortizations with adjustment of the outstanding loan balance
. . . 256
6.6.
Valuation of reserves in unshared loans
....................258
6.6.1.
General aspects
................................258
6.6.2.
Makeham s formula
.............................259
6.6.3.
Usufructs and bare ownership valuation for some
amortization forms
.................................262
6.7.
Leasing operation
.................................265
6.7.1.
Ordinary leasing
...............................265
6.7.2.
The monetary adjustment in leasing
...................268
6.8.
Amortizations of loans shared in securities
..................268
6.8.1.
An introduction on the securities
..................... 268
6.8.2.
Amortization from the viewpoint of the debtor
............. 270
6.8.3.
Amortization from the point of view of the bondholder
........ 271
6.8.4.
Drawing probabiity and mean life
..................... 272
6.8.5.
Adjustable rate bonds, indexed bonds and convertible bonds
.... 274
6.8.6.
Rule variations in bond loans
....................... 275
6.9.
Valuation in shared loans
............................. 276
6.9.1.
Introduction
................................. 276
6.9.2.
Valuation of bonds with given maturity
................. 277
6.9.3.
Valuation of drawing bonds
........................ 280
6.9.4.
Bond loan with varying rate or values adjusted in time
........ 286
Chapter
7.
Exchanges and Prices on the Financial Market
...........289
7.1.
A reinterpretation of the financial quantities in a market and price logic:
the perfect market
....................................289
7.1.1.
The perfect market
..............................289
7.1.2.
Bonds
.....................................291
7.2.
Spot contracts, price and rates. Yield rate
...................294
7.3.
Forward contracts, prices and rates
.......................302
7.4.
The implicit structure of prices, rates and intensities
............304
7.5.
Term structures
...................................310
7.5.1.
Structures with discrete payments
...................310
7.5.2.
Structures with fractional periods
.....................324
7.5.3.
Structures with flows in continuum
..................327
Chapter
8.
Annuities, Amortizations and Funding in the Case of
Term Structures
......................................331
8.1.
Capital value of annuities in the case of term structures
..........331
8.2.
Amortizations in the case of term structures
.................336
8.2.1.
Amortization with varying installments
.................337
Table
of Coatents
ix
8.2.2.
Amortization with constant installments
.................343
8.2.3.
Amortization with constant principal repayments
...........348
8.2.4.
Life amortization
...............................349
8.3.
Updating of valuations during amortization
..................352
8.4.
Funding in term structure environments
....................355
8.5.
Valuations referred to shared loans in term structure environments.
. . . 358
8.5.1.
Financial flows by the issuer s and investors point of view
.....359
8.5.2.
Valuations of price and yield
........................360
Chapter
9.
Time and Variability Indicators, Classical Immunization
.....363
9.1.
Main time indicators
...............................363
9.1.1.
Maturity and time to maturity
.......................364
9.1.2.
Arithmetic mean maturity
.........................364
9.1.3.
Average maturity
...............................364
9.1.4.
Mean financial time length or duration
................366
9.2.
Variability and dispersion indicators
......................374
9.2.1.
2nd order duration
..............................374
9.2.2.
Relative variation
..............................376
9.2.3.
Elasticity
...................................377
9.2.4.
Convexity and volatility convexity
....................377
9.2.5.
Approximated estimations of price fluctuation
.............380
9.3.
Rate risk and classicalimmunization
......................386
9.3.1.
An introductin to financial risk
...................... 386
9.3.2.
Preliminaries to classic immunization
.................. 392
9.3.3.
The optimal time of realization
...................... 393
9.3.4.
The meaning of classical immunization
................. 395
9.3.5.
Single liability cover
............................ 396
9.3.6.
Multiple liability cover
........................... 400
Part II. Stochastic Models
................................409
Chapter
10.
Basic Probabilistic Tools for Finance
.................411
10.1.
The sample space
.................................411
10.2.
Probability space
.................................412
10.3.
Random variables
................................417
10.4.
Expectation and independence
.........................421
10.5.
Main distribution probabilities
.........................425
10.5.1.
The binominal distribution
........................425
10.5.2.
The
Poisson
distribution
..........................426
10.5.3.
The normal (or Laplace Gauss) distribution
..............427
10.5.4.
The log-normal distribution
........................430
10.5.5.
The negative exponential distribution
..................432
χ
Mathematical Finance
10.5.6.
The multidimensional normal distribution
...............433
10.6.
Conditioning
...................................435
10.7.
Stochastic processes
...............................446
10.8.
Martingales
....................................450
10.9.
Brownian motion
.................................453
Chapter
11.
Markov Chains
...............................457
11.1.
Definitions
....................................457
11.2.
State classification
................................462
11.3.
Occupation times
.................................467
11.4.
Absorption probabilities
............................468
11.5
Asymptotic behavior
...............................469
11.6
Examples
......................................474
11.6.1.
A management problem in an insurance company
..........474
11.6.2.
A case study in social insurance
.....................476
Chapter
12.
Semi-Markov Processes
.........................481
12.1.
Positive
(J
-Х)
processes
.............................481
12.2.
Semi-Markov and extended semi-Markov chains
.............482
12.3.
Primary properties
................................484
12.4.
Examples
.....................................488
12.5.
Markov renewal processes, semi-Markov and associated
counting processes
...................................491
12.6.
Particular cases of MRP
.............................493
12.6.1.
Renewal processes and Markov chains
.................493
12.6.2.
MRP of zero order
.............................494
12.6.3.
Continuous Markov processes
......................495
12.7.
Markov renewal functions
...........................496
12.8.
The Markov renewal equation
.........................500
12.9.
Asymptotic behavior of an MRP
.......................502
12.10.
Asymptotic behavior of SMP
.........................503
12.10.1.
Irreducible case
.............................. 503
12.10.2.
Non-irreducible case
........................... 506
12.11.
Non-homogenous Markov and semi-Markov processes
......... 508
12.11.1.
General definitions
............................ 508
Chapter
13.
Stochastic or
M
Calculus
........................517
13.1.
Problem of stochastic integration
....................... 517
13.2.
Stochastic integration of simple predictable processes and
semi-martingales
.................................... 519
13.3.
General definition of the stochastic integral
................. 523
Table
of
Contents xi
13.4.
Itô s formula
...................................529
13.4.1.
Quadratic
variation
of
a
semi-martingale
................529
13.4.2.
Itô s formula
................................531
13.5.
Stochastic integral with standard Brownian motion as
integrator process
.................................... 532
13.5.1.
Case of predictable simple processes
.................. 533
13.5.2.
Extension to general integrand processes
................ 535
13.6.
Stochastic differentiation
............................ 536
13.6.1.
Definition
..................................536
13.6.2.
Examples
..................................536
13.7. Backte
Itô s
formula
..............................537
13.7.1.
Stochastic differential of a product
................... 537
13.7.2.
Itô s
formula with time dependence
................... 538
13.7.3.
Interpretation of
Itô s
formula
...................... 540
13.7.4.
Other extensions of
Itô s
formula
.................... 540
13.8.
Stochastic differential equations
........................ 545
13.8.1.
Existence and unicity general thorem
..................545
13.8.2.
Solution of stochastic differntial equations
...............549
13.9.
Diffusion processes
...............................550
Chapter
14.
Option Theory
...............................553
14.1.
Introduction
....................................553
14.2.
The Cox, Ross, Rubinstein (CRR) or binomial model
...........557
14.2.1.
One-period model
.............................557
14.2.2.
Multi-period model
............................561
14.3.
The Black-Scholes formula as the limit of the binomial model
.....564
14.3.1.
The lognormality of the underlying asset
................564
14.3.2.
The Black-Scholes formula
........................567
14.4.
The Black-Scholes continuous time model
.................568
14.4.1.
The model
.................................. 568
14.4.2.
The Solution of the Black-Scholes-Samuelson model
........ 569
14.4.3.
Pricing the call with the Black-Scholes-Samuelson model
..... 570
14.5.
Exercises on option pricing
........................... 576
14.6.
The Greek parameters
.............................. 577
14.6.1.
Introduction
................................. 577
14.6.2.
Values of the Greek parameters
..................... 579
14.6.3.
Excercises
.................................. 581
14.7.
The impact of dividend repartition
...................... 583
14.8.
Estimation of the volatility
........................... 584
14.8.1.
Historic method
...............................584
14.8.2.
Implicit volatility method
.........................586
14.9.
Black-Scholes on the market
..........................587
xii
Mathematical Finance
14.9.1.
Empirical studies
..............................587
14.9.2.
Smile effect
.................................587
14.10.
Exotic options
..................................588
14.10.1.
Introduction
................................ 588
14.10.2.
Garman-Kohlhagen formula
...................... 589
14.10.3.
Greek parameters
............................. 590
14.10.4.
Theoretical models
............................ 590
14.10.5.
Binary or digital options
......................... 592
14.10.6.
Asset or nothing options
....................... 595
14.10.7.
The barrier options
............................ 599
14.10.8.
Lockback
options
............................. 601
14.10.9.
Asiatic (or average) options
....................... 601
14.10.10.
Rainbow options
.............................602
14.11.
The formula of Barone-Adesi and Whaley
(1987):
formula
for American options
..................................603
Chapter
15.
Markov and Semi-Markov Option Models
.............607
15.1.
The
Janssen-Manca
model
...........................607
15.1.1.
The Markov extension of the one-period CRR model
........608
15.1.2.
The multi-period discrete Markov chain model
............616
15.1.3.
The multi-period discrete Markov chain limit model
.........619
15.1.4.
The extension of the Black-Scholes pricing formula with
Markov environment: the
Janssen-Manca
formula
...............621
15.2.
The extension of the Black-Scholes pricing formula with a
semi-Markov environment: the
Janssen-Manca-Volpe
formula
.........624
15.2.1.
Introduction
.................................624
15.2.2.
The
Janssen-Manca-Çinlar
model
....................625
15.2.3.
Call option pricing
.............................628
15.2.4.
Stationary option pricing formula
....................630
15.3.
Markov and semi-Markov option pricing models with arbitrage
possibility
........................................631
15.3.1.
Introduction
.................................631
15.3.2.
The homogenous Markov model for the underlying asset
......633
15.3.3.
Particular cases
...............................634
15.3.4.
Numerical example for the Markov model
...............635
15.3.5.
The continuous time homogenous semi-Markov model for
the underlying asset
.................................637
15.3.6.
Numerical example for the semi-Markov model
...........639
15.3.7.
Conclusion
..................................640
Table of
Contents xiii
Chapter
16.
Interest Rate Stochastic Models
-
Application to the
Bond Pricing Problem
..................................641
16.1.
The bond investments
..............................641
16.1.1.
Introduction
.................................641
16.1.2.
Yield curve
.................................642
16.1.3.
Yield to maturity for a financial investment and for a bond
.....643
16.2.
Dynamic deterministic continuous time model for instantaneous
interesirate
........................................644
16.2.1.
Instantaneous
interesirate
.........................644
16.2.2.
Particular cases
...............................645
16.2.3.
Yield curve associated with instantaneous interest rate
.......645
16.2.4.
Example of theoretical models
......................646
16.3.
Stochastic continuous time dynamic model for instantaneous
interesirate
........................................648
16.3.1.
The OUV stochastic model
........................ 649
16.3.2.
The
CIR
model
(1985)........................... 655
16.3.3.
The HJM model
(1992).......................... 658
16.4.
Zero-coupon pricing under the assumption of no arbitrage
........ 666
16.4.1.
Stochastic dynamics of zero-coupons
..................667
16.4.2.
Application of the no arbitrage principle and risk premium
.....668
16.4.3.
Partial differential equatin for the structure of zero coupons
.... 670
16.4.4.
Values of zero coupons without arbitrage opportunity
for particular cases
................................. 672
16.4.5.
Values of a call on zero-coupon
..................... 681
16.4.6.
Option on bond with coupons
...................... 682
16.4.7.
A numerical example
........................... 683
16.5.
Appendix (solution of the OUV equation)
................. 684
Chapter
17.
Portfolio Theory
..............................687
17.1.
Quantitative portfolio management
...................... 687
17.2.
Notion of efficiency
............................... 688
17.3.
Exercises
...................................... 693
17.4. Markowitz
theory for two assets
........................ 694
17.5.
Case of one risky asset and one non-risky asset
............... 698
Chapter
18.
Value at Risk (VaR) Methods and Simulation
...........703
18.1.
VaR of one asset
................................. 703
18.1.1.
Introduction
................................. 703
18.1.2.
Definition ofVaR for one asset
..................... 704
18.1.3.
Case of the normal distribution
..................... 705
xiv
Mathematical Finance
18.1.4.
Example II: an internal model in case of the lognormal
distribution
......................................707
18.1.5.
Trajectory simulation
...........................712
18.2.
Coherence and VaR extensions
........................712
18.2.1.
Risk measures
................................712
18.2.2.
General form of the VaR
.........................713
18.2.3.
VaR extensions: TVaR and conditional VaR
.............716
18.3.
VaR of an asset portfolio
............................721
18.3.1.
VaR methodology
.............................722
18.3.2.
General methods for VaR calculation
..................724
18.3.3.
VaR implementation
............................725
18.3.4.
VaR for a bond portfolio
.........................732
18.4.
VaR for one plain vanilla option
........................734
18.5.
VaR and Monte Carlo simulation methods
.................737
18.5.1.
Introduction
.................................737
18.5.2.
Case of one risk factor
...........................737
18.5.3.
Case of several risk factors
........................738
18.5.4.
Monte Carlo simulation scheme for the VaR calculation of
an asset portfolio
...................................741
Chapter
19.
Credit Risk or Default Risk
.......................743
19.1.
Introduction
....................................743
19.2.
The Merton model
................................744
19.2.1.
Evaluation model of a risky debt
.....................744
19.2.2.
Interpretation of Merton s result
.....................746
19.2.3.
Spreads
....................................747
19.3.
The Longstaffand Schwartz model
(1995).................750
19.4.
Construction of a rating with Merton
s
model for the firm
........752
19.4.1.
Rating construction
............................752
19.4.2.
Time dynamic evolution of a rating
...................756
19.5.
Discrete time semi-Markov processes
....................763
19.5.1.
Purpose
....................................763
19.5.2.
DTSMP definition
.............................765
19.6.
Semi-Markov credit risk models
........................768
19.7.
NHSMP with backward conditioning time
.................770
19.8.
Examples
.....................................772
19.8.1.
Homogenous SMP application
......................772
19.8.2.
Non-homogenous downward example
.................776
19.8.3.
Non-homogenous downward backward example
...........784
Table of
Contents xv
Chapter
20.
Markov and Semi-Markov Reward Processes and
Stochastic Annuities
.................................... 791
20.1.
Reward processes
................................ 791
20.2.
Homogenous and non-homogenous DTMRWP
............... 795
20.3.
Homogenous and non-homogenous DTSMRWP
.............. 799
20.3.1.
The immediate cases
............................ 799
20.3.2.
The due cases
................................ 807
20.4.
MRWP and stochastic annuities
........................ 811
20.4.1.
Stochastic annuities
............................ 811
20.4.2.
Motorcar insurance application
..................... 814
20.5.
DTSMRWP and generalized stochastic annuities (GSA)
......... 822
20.5.1.
Generalized stochastic annuities (GSA)
................ 822
20.5.2.
GSA examples
............................... 824
References
..........................................831
Index
.............................................839
|
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| id | DE-604.BV035297885 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T21:30:43Z |
| institution | BVB |
| isbn | 9781848210813 1848210817 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017102809 |
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| spelling | Mathematical finance deterministic and stochastic models Jacques Janssen ; Raimondo Manca ; Ernesto Volpe di Prignano 1. publ. London ISTE [u.a.] 2009 XX, 852 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Literaturverz. S. 831 - 837 Finances - Modèles mathématiques Finances - Modèles mathématiques ram Finanzmathematik stw Investissements - Mathématiques Investissements - Mathématiques ram Processus stochastiques Processus stochastiques ram Mathematik Mathematisches Modell Finance Mathematical models Stochastic processes Investments Mathematics Finanzmathematik (DE-588)4017195-4 gnd rswk-swf (DE-588)4006432-3 Bibliografie gnd-content (DE-588)4123623-3 Lehrbuch gnd-content Finanzmathematik (DE-588)4017195-4 s DE-604 Janssen, Jacques 1939- Sonstige (DE-588)136691331 oth Manca, Raimondo Sonstige (DE-588)136691420 oth Volpe di Prignano, Ernesto Sonstige oth Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017102809&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mathematical finance deterministic and stochastic models Finances - Modèles mathématiques Finances - Modèles mathématiques ram Finanzmathematik stw Investissements - Mathématiques Investissements - Mathématiques ram Processus stochastiques Processus stochastiques ram Mathematik Mathematisches Modell Finance Mathematical models Stochastic processes Investments Mathematics Finanzmathematik (DE-588)4017195-4 gnd |
| subject_GND | (DE-588)4017195-4 (DE-588)4006432-3 (DE-588)4123623-3 |
| title | Mathematical finance deterministic and stochastic models |
| title_auth | Mathematical finance deterministic and stochastic models |
| title_exact_search | Mathematical finance deterministic and stochastic models |
| title_full | Mathematical finance deterministic and stochastic models Jacques Janssen ; Raimondo Manca ; Ernesto Volpe di Prignano |
| title_fullStr | Mathematical finance deterministic and stochastic models Jacques Janssen ; Raimondo Manca ; Ernesto Volpe di Prignano |
| title_full_unstemmed | Mathematical finance deterministic and stochastic models Jacques Janssen ; Raimondo Manca ; Ernesto Volpe di Prignano |
| title_short | Mathematical finance |
| title_sort | mathematical finance deterministic and stochastic models |
| title_sub | deterministic and stochastic models |
| topic | Finances - Modèles mathématiques Finances - Modèles mathématiques ram Finanzmathematik stw Investissements - Mathématiques Investissements - Mathématiques ram Processus stochastiques Processus stochastiques ram Mathematik Mathematisches Modell Finance Mathematical models Stochastic processes Investments Mathematics Finanzmathematik (DE-588)4017195-4 gnd |
| topic_facet | Finances - Modèles mathématiques Finanzmathematik Investissements - Mathématiques Processus stochastiques Mathematik Mathematisches Modell Finance Mathematical models Stochastic processes Investments Mathematics Bibliografie Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017102809&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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