Essentials of stochastic finance: facts, models, theory
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| Language: | English |
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Singapore [u.a.]
World Scientific
2008
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| Edition: | Repr. |
| Series: | Advanced series on statistical science & applied probability
3 |
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| Online Access: | Inhaltsverzeichnis |
| Item Description: | Aus dem Russ. übers. |
| Physical Description: | XVI, 834 S. graph. Darst. |
| ISBN: | 9810236050 9789810236052 |
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| 245 | 1 | 0 | |a Essentials of stochastic finance |b facts, models, theory |c Albert N. Shiryaev |
| 250 | |a Repr. | ||
| 264 | 1 | |a Singapore [u.a.] |b World Scientific |c 2008 | |
| 300 | |a XVI, 834 S. |b graph. Darst. | ||
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| 490 | 1 | |a Advanced series on statistical science & applied probability |v 3 | |
| 500 | |a Aus dem Russ. übers. | ||
| 650 | 4 | |a Finanzmathematik - Stochastischer Prozess | |
| 650 | 4 | |a Stochastisches Modell - Kreditmarkt - Financial Engineering | |
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| adam_text | Contents
Foreword
................................................................ xiii
Part
1.
Facts. Models
1
Chapter I. Main Concepts, Structures, and Instruments.
Aims and Problems of Financial Theory
and Financial Engineering
2
1.
Financial structures and instruments
........................... 3
§
la. Key objects and structures
............................. 3
§
lb. Financial markets
................................... 6
§
lc. Market of derivatives. Financial instruments
................ 20
2.
Financial markets under uncertainty. Classical theories of
the dynamics of financial indexes, their critics and revision.
Neoclassical theories
............................................... 35
§
2a. Random walk conjecture and concept of efficient market
....... 37
§
2b. Investment portfolio. Markowitz s diversification
............. 46
§
2c. CAPM: Capital Asset Pricing Model
..................... 51
§
2d. APT: Arbitrage Pricing Theory
......................... 56
§
2e. Analysis, interpretation, and revision of the classical concepts
of efficient market. I
.................................. 60
§
2f. Analysis, interpretation, and revision of the classical concepts
of efficient market. II
................................. 65
3.
Aims and problems of financial theory, engineering,
and actuarial calculations
......................................... 69
§
3a. Role of financial theory and financial engineering. Financial risks
69
§
3b. Insurance: a social mechanism of compensation for financial losses
71
§
3c. A classical example of actuarial calculations: the
Lundberg-Cramér
theorem
.......................................... 77
Chapter II. Stochastic Models. Discrete Time
80
1.
Necessary probabilistic concepts and several models
of the dynamics of market prices
................................. 81
§
la. Uncertainty and irregularity in the behavior of prices.
Their description and representation in probabilistic terms
..... 81
§
lb. Doob decomposition. Canonical representations
............. 89
§
lc. Local martingales. Martingale transformations. Generalized
martingales
........................................ 95
§
Id. Gaussian and conditionally Gaussian models
................ 103
§
le.
Binomial model of price evolution
........................ 109
§
If. Models with discrete intervention of chance
................. 112
2.
Linear stochastic models
.......................................... 117
§
2a. Moving average model MA(q)
........................... 119
§
2b.
Autoregressive
model AR(p)
........................... 125
§
2c.
Autoregressive
and moving average model ARMA(p, q)
and integrated model ARIMA(p, d,q)
..................... 138
§
2d. Prediction in linear models
............................. 142
3.
Nonlinear stochastic conditionally Gaussian models
.......... 152
§
3a. ARCH and
GARCIÍ
models
........................... 153
§
3b. EG ARCH, TGARCH, HARCH, and other models
............ 163
§
3c. Stochastic volatility models
............................ 168
4.
Supplement: dynamical chaos models
........................... 176
§
4a. Nonlinear chaotic models
.............................. 176
§
4b. Distinguishing between chaotic and stochastic sequences
..... 183
Chapter III. Stochastic Models. Continuous Time
188
1.
Non-Gaussian models of distributions and processes
.......... 189
§
la. Stable and infinitely divisible distributions
................. 189
§
lb. Levy processes
...................................... 200
§
lc. Stable processes
..................................... 207
§
Id. Hyperbolic distributions and processes
.................... 214
2.
Models with self-similarity. Fractality
.......................... 221
§
2a. Hurst s statistical phenomenon of self-similarity
............. 221
§
2b. A digression on fractal geometry
........................ 224
§
2c. Statistical self-similarity. Fractal Brownian motion
........... 226
§
2d. Fractional Gaussian noise: a process with strong aftereffect
..... 232
3.
Models based on a Brownian motion
............................. 236
§
3a. Brownian motion and its role of a basic process
............. 236
§
3b. Brownian motion: a compendium of classical results
.......... 240
§
3c. Stochastic integration with respect to a Brownian motion
...... 251
§ 3d.
Ito
processes and
Itô s
formula
.......................... 257
§
3e. Stochastic differential equations
......................... 264
§
3f. Forward and backward Kolmogorov s equations. Probabilistic
representation of solutions
............................. 271
4.
Diffusion models of the evolution of interest rates, stock and
bond prices
.......................................................... 278
§4a. Stochastic interest rates
............................... 278
§
4b. Standard diffusion model of stock prices (geometric Brownian
motion) and its generalizations
.......................... 284
§
4c. Diffusion models of the term structure of prices in a family of bonds
289
5.
Semimartingale
models
............................................ 294
§
5a. Semimartingales and stochastic integrals
................... 294
§
5b. Doob-Meyer decomposition. Compensators. Quadratic variation
. 301
§
5c.
Itô s
formula for semimartingales. Generalizations
............ 307
Chapter IV. Statistical Analysis of Financial Data
314
1.
Empirical data. Probabilistic and statistical models
of their description. Statistics of ticks
......................... 315
§
la. Structural changes in financial data gathering and analysis
..... 315
§
lb. Geography-related features of the statistical data on exchange rates
318
§
lc. Description of financial indexes as stochastic processes
with discrete intervention of chance
...................... 321
§
Id. On the statistics of ticks
............................. 324
2.
Statistics of one-dimensional distributions
..................... 327
§
2a. Statistical data discretizing
............................ 327
§
2b. One-dimensional distributions of the logarithms of relative
price changes. Deviation from the Gaussian property
and leptokurtosis of empirical densities
.................... 329
§
2c. One-dimensional distributions of the logarithms of relative
price changes. Heavy tails and their statistics
.............. 334
§
2d. One-dimensional distributions of the logarithms of relative
price changes. Structure of the central parts of distributions
.... 340
3.
Statistics of volatility, correlation dependence,
and aftereffect in prices
............................................ 345
§
3a. Volatility. Definition and examples
....................... 345
§
3b. Periodicity and fractal structure of volatility in exchange rates
. . 351
§
Зс.
Correlation properties
................................ 354
§ 3d.
Devolatization . Operational time
....................... 358
§
3e. Cluster phenomenon and aftereffect in prices
............... 364
4.
Statistical
Тг/5
-analysis
............................................ 367
§
4a. Sources and methods of Tl/S-analysis
..................... 367
§
4b. 7£/<S~analysis of some financial time series
................. 376
Part
2.
Theory
381
Chapter V. Theory of Arbitrage in Stochastic Financial Models.
Discrete Time
382
1.
Investment portfolio on
a (JE?,
iS)-market
......................... 383
§
la. Strategies satisfying balance conditions
.................... 383
§
lb. Notion of hedging . Upper and lower prices.
Complete and incomplete markets
....................... 395
§
lc. Upper and lower prices in a single-step model
............... 399
§
Id,
CAiž-model:
an example of a complete market
.............. 408
2.
Arbitrage-free market
.............................................. 410
§
2a. Arbitrage and absence of arbitrage
..................... 410
§
2b. Martingale criterion of the absence of arbitrage.
First fundamental theorem
............................. 413
§
2c. Martingale criterion of the absence of arbitrage.
Proof of sufficiency
.................................. 417
§
2d. Martingale criterion of the absence of arbitrage.
Proof of necessity (by means of the Esscher conditional
transformation)
..................................... 417
§
2e. Extended version of the First fundamental theorem
........... 424
3.
Construction of martingale measures
by means of an absolutely continuous change of measure
___ 433
§
3a. Main definitions. Density process
........................ 433
§3b. Discrete version of Girsanov s theorem. Conditionally Gaussian case
439
§
3c. Martingale property of the prices in the case of a conditionally
Gaussian and logarithmically conditionally Gaussian distributions
446
§ 3d.
Discrete version of Girsanov s theorem. General case
......... 450
§
3e. Integer-valued random measures and their compensators.
Transformation of compensators under absolutely continuous
changes of measures. Stochastic integrals
................. 459
§
3f. Predictable criteria of arbitrage-free (B, S^-markets
.......... 467
4.
Complete
and perfect arbitrage-free markets
.................. 481
§
4a. Martingale criterion of a complete market.
Statement of the Second fundamental theorem. Proof of necessity
481
§
4b. Representability of local martingales.
Ä-representability ...... 483
§
4c. Representability of local martingales
( ^-representability and
(μ—
i^-representability )
............ 485
§4d. S -representability in the binomial
CÄÄ-model ............. 488
§
4e. Martingale criterion of a complete market.
Proof of necessity for
d
= 1 ............................ 491
§
4f. Extended version of the Second fundamental theorem
......... 497
Chapter VI. Theory of Pricing in Stochastic Financial Models.
Discrete Time
502
1.
European hedge pricing on arbitrage-free markets
............ 503
§
la. Risks and their reduction
.............................. 503
§
lb. Main hedge pricing formula. Complete markets
............. 505
§
lc. Main hedge pricing formula. Incomplete markets
............. 512
§
Id. Hedge pricing on the basis of the mean square criterion
........ 518
§
le.
Forward contracts and futures contracts
................... 521
2.
American hedge pricing on arbitrage-free markets
............ 525
§
2a. Optimal stopping problems.
Supermartingale
characterization
. . . 525
§
2b. Complete and incomplete markets.
Supermartingale
characterization of hedging prices
........... 535
§
2c. Complete and incomplete markets.
Main formulas for hedging prices
........................ 538
§
2d. Optional decomposition
............................... 546
3.
Scheme of series of large arbitrage-free markets
and asymptotic arbitrage
......................................... 553
§
3a. One model of large financial markets
.................... 553
§
3b. Criteria of the absence of asymptotic arbitrage
.............. 555
§
3c. Asymptotic arbitrage and contiguity
...................... 559
§ 3d.
Some issues of approximation and convergence in the scheme
of series of arbitrage-free markets
........................ 575
4.
European options on a binomial (S, 5)-market
................. 588
§
4a. Problems of option pricing
............................. 588
§
4b. Rational pricing and hedging strategies.
Pay-off function of the general form
...................... 590
§
4c. Rational pricing and hedging strategies.
Markovian pay-off functions
............................ 595
§
4d. Standard
call and put options
.......................... 598
§
4e. Option-based strategies (combinations and spreads)
.......... 604
5.
American options on a binomial (B, S )-market
................. 608
§
5a. American option pricing
............................... 608
§
5b. Standard call option pricing
............................ 611
§50.
Standard put option pricing
............................ 621
§
5d. Options with aftereffect. Russian option pricing
............ 625
Chapter
VII.
Theory of Arbitrage in Stochastic Financial Models.
Continuous Time
632
1.
Investment portfolio in
semimartingale
models
................ 633
§
la. Admissible strategies. Self-financing. Stochastic vector integral
. . 633
§
lb. Discounting processes
................................ 643
§
lc. Admissible strategies. Some special classes
................. 646
2.
Semimartingale
models without opportunities for arbitrage.
Completeness
....................................................... 649
§
2a. Concept of absence of arbitrage and its modifications
......... 649
§
2b. Martingale criteria of the absence of arbitrage.
Sufficient conditions
.................................. 651
§
2c. Martingale criteria of the absence of arbitrage.
Necessary and sufficient conditions (a list of results)
.......... 655
§
2d. Completeness in
semimartingale
models
................... 660
3.
Semimartingale
and martingale measures
...................... 662
§
3a. Canonical representation of semimartingales.
Random measures. Triplets of predictable characteristics
...... 662
§
3b. Construction of martingale measures in
diffusion
models.
Girsanov s theorem
.................................. 672
§
3c. Construction of martingale measures for Levy processes.
Esscher transformation
............................... 683
§ 3d.
Predictable criteria of the martingale property of prices. I
...... 691
§
3e. Predictable criteria of the martingale property of prices. II
..... 694
§
3f. Representability of local martingales ( (if0,
μ—
i^-representability )
698
§
3g. Girsanov s theorem for semimartingales.
Structure of the densities of probabilistic measures
........... 701
4.
Arbitrage, completeness, and hedge pricing in diffusion
models of stock
...................................................... 704
§
4a. Arbitrage and conditions of its absence. Completeness
........ 704
§
4b. Price of hedging in complete markets
..................... 709
§
4c. Fundamental partial differential equation of hedge pricing
...... 712
5. Arbitrage,
completeness, and hedge pricing in diffusion
models of bonds
..................................................... 717
§5a. Models without opportunities for arbitrage
................. 717
§
5b. Completeness
...................................... 728
§
5c. Fundamental partial differentai equation of the term structure
of bonds
.......................................... 730
Chapter
VIII.
Theory of Pricing in Stochastic Financial Models.
Continuous Time
734
1.
European options in diffusion (B, S^-stockmarkets
............. 735
§
la. Bachelier s formula
.................................. 735
§
lb. Black-Scholes formula. Martingale inference
................ 739
§
lc. Black-Scholes formula. Inference based on the solution
of the fundamental equation
............................ 745
§
Id. Black-Scholes formula. Case with dividends
................ 748
2.
American options in diffusion (B. 5)-stockmarkets.
Case of an infinite time horizon
................................... 751
§
2a. Standard call option
................................. 751
§
2b. Standard put option
................................. 763
§
2c. Combinations of put and call options
..................... 765
§
2d. Russian option
..................................... 767
3.
American options in diffusion (B, 5 )-stockmarkets.
Finite time horizons
................................................ 778
§
3a. Special features of calculations on finite time intervals
......... 778
§
3b. Optimal stopping problems and
Stephan
problems
........... 782
§
3c.
Stephan
problem for standard call and put options
........... 784
§ 3d.
Relations between the prices of European and American options
. 788
4.
European and American options in a diffusion
(B, P)-bondmarket
.................................................. 792
§
4a. Option pricing in a bondmarket
......................... 792
§
4b. European option pricing in single-factor Gaussian models
...... 795
§
4c. American option pricing in single-factor Gaussian models
...... 799
Bibliography
........................................................... 803
Index
.................................................................... 825
Index of symbols
....................................................... 833
|
| adam_txt |
Contents
Foreword
. xiii
Part
1.
Facts. Models
1
Chapter I. Main Concepts, Structures, and Instruments.
Aims and Problems of Financial Theory
and Financial Engineering
2
1.
Financial structures and instruments
. 3
§
la. Key objects and structures
. 3
§
lb. Financial markets
. 6
§
lc. Market of derivatives. Financial instruments
. 20
2.
Financial markets under uncertainty. Classical theories of
the dynamics of financial indexes, their critics and revision.
Neoclassical theories
. 35
§
2a. Random walk conjecture and concept of efficient market
. 37
§
2b. Investment portfolio. Markowitz's diversification
. 46
§
2c. CAPM: Capital Asset Pricing Model
. 51
§
2d. APT: Arbitrage Pricing Theory
. 56
§
2e. Analysis, interpretation, and revision of the classical concepts
of efficient market. I
. 60
§
2f. Analysis, interpretation, and revision of the classical concepts
of efficient market. II
. 65
3.
Aims and problems of financial theory, engineering,
and actuarial calculations
. 69
§
3a. Role of financial theory and financial engineering. Financial risks
69
§
3b. Insurance: a social mechanism of compensation for financial losses
71
§
3c. A classical example of actuarial calculations: the
Lundberg-Cramér
theorem
. 77
Chapter II. Stochastic Models. Discrete Time
80
1.
Necessary probabilistic concepts and several models
of the dynamics of market prices
. 81
§
la. Uncertainty and irregularity in the behavior of prices.
Their description and representation in probabilistic terms
. 81
§
lb. Doob decomposition. Canonical representations
. 89
§
lc. Local martingales. Martingale transformations. Generalized
martingales
. 95
§
Id. Gaussian and conditionally Gaussian models
. 103
§
le.
Binomial model of price evolution
. 109
§
If. Models with discrete intervention of chance
. 112
2.
Linear stochastic models
. 117
§
2a. Moving average model MA(q)
. 119
§
2b.
Autoregressive
model AR(p)
. 125
§
2c.
Autoregressive
and moving average model ARMA(p, q)
and integrated model ARIMA(p, d,q)
. 138
§
2d. Prediction in linear models
. 142
3.
Nonlinear stochastic conditionally Gaussian models
. 152
§
3a. ARCH and
GARCIÍ
models
. 153
§
3b. EG ARCH, TGARCH, HARCH, and other models
. 163
§
3c. Stochastic volatility models
. 168
4.
Supplement: dynamical chaos models
. 176
§
4a. Nonlinear chaotic models
. 176
§
4b. Distinguishing between 'chaotic' and 'stochastic' sequences
. 183
Chapter III. Stochastic Models. Continuous Time
188
1.
Non-Gaussian models of distributions and processes
. 189
§
la. Stable and infinitely divisible distributions
. 189
§
lb. Levy processes
. 200
§
lc. Stable processes
. 207
§
Id. Hyperbolic distributions and processes
. 214
2.
Models with self-similarity. Fractality
. 221
§
2a. Hurst's statistical phenomenon of self-similarity
. 221
§
2b. A digression on fractal geometry
. 224
§
2c. Statistical self-similarity. Fractal Brownian motion
. 226
§
2d. Fractional Gaussian noise: a process with strong aftereffect
. 232
3.
Models based on a Brownian motion
. 236
§
3a. Brownian motion and its role of a basic process
. 236
§
3b. Brownian motion: a compendium of classical results
. 240
§
3c. Stochastic integration with respect to a Brownian motion
. 251
§ 3d.
Ito
processes and
Itô's
formula
. 257
§
3e. Stochastic differential equations
. 264
§
3f. Forward and backward Kolmogorov's equations. Probabilistic
representation of solutions
. 271
4.
Diffusion models of the evolution of interest rates, stock and
bond prices
. 278
§4a. Stochastic interest rates
. 278
§
4b. Standard diffusion model of stock prices (geometric Brownian
motion) and its generalizations
. 284
§
4c. Diffusion models of the term structure of prices in a family of bonds
289
5.
Semimartingale
models
. 294
§
5a. Semimartingales and stochastic integrals
. 294
§
5b. Doob-Meyer decomposition. Compensators. Quadratic variation
. 301
§
5c.
Itô's
formula for semimartingales. Generalizations
. 307
Chapter IV. Statistical Analysis of Financial Data
314
1.
Empirical data. Probabilistic and statistical models
of their description. Statistics of 'ticks'
. 315
§
la. Structural changes in financial data gathering and analysis
. 315
§
lb. Geography-related features of the statistical data on exchange rates
318
§
lc. Description of financial indexes as stochastic processes
with discrete intervention of chance
. 321
§
Id. On the statistics of 'ticks'
. 324
2.
Statistics of one-dimensional distributions
. 327
§
2a. Statistical data discretizing
. 327
§
2b. One-dimensional distributions of the logarithms of relative
price changes. Deviation from the Gaussian property
and leptokurtosis of empirical densities
. 329
§
2c. One-dimensional distributions of the logarithms of relative
price changes. 'Heavy tails' and their statistics
. 334
§
2d. One-dimensional distributions of the logarithms of relative
price changes. Structure of the central parts of distributions
. 340
3.
Statistics of volatility, correlation dependence,
and aftereffect in prices
. 345
§
3a. Volatility. Definition and examples
. 345
§
3b. Periodicity and fractal structure of volatility in exchange rates
. . 351
§
Зс.
Correlation properties
. 354
§ 3d.
'Devolatization'. Operational time
. 358
§
3e. 'Cluster' phenomenon and aftereffect in prices
. 364
4.
Statistical
Тг/5
-analysis
. 367
§
4a. Sources and methods of Tl/S-analysis
. 367
§
4b. 7£/<S~analysis of some financial time series
. 376
Part
2.
Theory
381
Chapter V. Theory of Arbitrage in Stochastic Financial Models.
Discrete Time
382
1.
Investment portfolio on
a (JE?,
iS)-market
. 383
§
la. Strategies satisfying balance conditions
. 383
§
lb. Notion of 'hedging'. Upper and lower prices.
Complete and incomplete markets
. 395
§
lc. Upper and lower prices in a single-step model
. 399
§
Id,
CAiž-model:
an example of a complete market
. 408
2.
Arbitrage-free market
. 410
§
2a. 'Arbitrage' and 'absence of arbitrage'
. 410
§
2b. Martingale criterion of the absence of arbitrage.
First fundamental theorem
. 413
§
2c. Martingale criterion of the absence of arbitrage.
Proof of sufficiency
. 417
§
2d. Martingale criterion of the absence of arbitrage.
Proof of necessity (by means of the Esscher conditional
transformation)
. 417
§
2e. Extended version of the First fundamental theorem
. 424
3.
Construction of martingale measures
by means of an absolutely continuous change of measure
_ 433
§
3a. Main definitions. Density process
. 433
§3b. Discrete version of Girsanov's theorem. Conditionally Gaussian case
439
§
3c. Martingale property of the prices in the case of a conditionally
Gaussian and logarithmically conditionally Gaussian distributions
446
§ 3d.
Discrete version of Girsanov's theorem. General case
. 450
§
3e. Integer-valued random measures and their compensators.
Transformation of compensators under absolutely continuous
changes of measures. 'Stochastic integrals'
. 459
§
3f. 'Predictable' criteria of arbitrage-free (B, S^-markets
. 467
4.
Complete
and perfect arbitrage-free markets
. 481
§
4a. Martingale criterion of a complete market.
Statement of the Second fundamental theorem. Proof of necessity
481
§
4b. Representability of local martingales.
'Ä-representability' . 483
§
4c. Representability of local martingales
('^-representability' and
'(μ—
i^-representability')
. 485
§4d. 'S'-representability' in the binomial
CÄÄ-model . 488
§
4e. Martingale criterion of a complete market.
Proof of necessity for
d
= 1 . 491
§
4f. Extended version of the Second fundamental theorem
. 497
Chapter VI. Theory of Pricing in Stochastic Financial Models.
Discrete Time
502
1.
European hedge pricing on arbitrage-free markets
. 503
§
la. Risks and their reduction
. 503
§
lb. Main hedge pricing formula. Complete markets
. 505
§
lc. Main hedge pricing formula. Incomplete markets
. 512
§
Id. Hedge pricing on the basis of the mean square criterion
. 518
§
le.
Forward contracts and futures contracts
. 521
2.
American hedge pricing on arbitrage-free markets
. 525
§
2a. Optimal stopping problems.
Supermartingale
characterization
. . . 525
§
2b. Complete and incomplete markets.
Supermartingale
characterization of hedging prices
. 535
§
2c. Complete and incomplete markets.
Main formulas for hedging prices
. 538
§
2d. Optional decomposition
. 546
3.
Scheme of series of 'large' arbitrage-free markets
and asymptotic arbitrage
. 553
§
3a. One model of 'large' financial markets
. 553
§
3b. Criteria of the absence of asymptotic arbitrage
. 555
§
3c. Asymptotic arbitrage and contiguity
. 559
§ 3d.
Some issues of approximation and convergence in the scheme
of series of arbitrage-free markets
. 575
4.
European options on a binomial (S, 5)-market
. 588
§
4a. Problems of option pricing
. 588
§
4b. Rational pricing and hedging strategies.
Pay-off function of the general form
. 590
§
4c. Rational pricing and hedging strategies.
Markovian pay-off functions
. 595
§
4d. Standard
call and put options
. 598
§
4e. Option-based strategies (combinations and spreads)
. 604
5.
American options on a binomial (B, S')-market
. 608
§
5a. American option pricing
. 608
§
5b. Standard call option pricing
. 611
§50.
Standard put option pricing
. 621
§
5d. Options with aftereffect. 'Russian option' pricing
. 625
Chapter
VII.
Theory of Arbitrage in Stochastic Financial Models.
Continuous Time
632
1.
Investment portfolio in
semimartingale
models
. 633
§
la. Admissible strategies. Self-financing. Stochastic vector integral
. . 633
§
lb. Discounting processes
. 643
§
lc. Admissible strategies. Some special classes
. 646
2.
Semimartingale
models without opportunities for arbitrage.
Completeness
. 649
§
2a. Concept of absence of arbitrage and its modifications
. 649
§
2b. Martingale criteria of the absence of arbitrage.
Sufficient conditions
. 651
§
2c. Martingale criteria of the absence of arbitrage.
Necessary and sufficient conditions (a list of results)
. 655
§
2d. Completeness in
semimartingale
models
. 660
3.
Semimartingale
and martingale measures
. 662
§
3a. Canonical representation of semimartingales.
Random measures. Triplets of predictable characteristics
. 662
§
3b. Construction of martingale measures in
diffusion
models.
Girsanov's theorem
. 672
§
3c. Construction of martingale measures for Levy processes.
Esscher transformation
. 683
§ 3d.
Predictable criteria of the martingale property of prices. I
. 691
§
3e. Predictable criteria of the martingale property of prices. II
. 694
§
3f. Representability of local martingales ('(if0,
μ—
i^-representability')
698
§
3g. Girsanov's theorem for semimartingales.
Structure of the densities of probabilistic measures
. 701
4.
Arbitrage, completeness, and hedge pricing in diffusion
models of stock
. 704
§
4a. Arbitrage and conditions of its absence. Completeness
. 704
§
4b. Price of hedging in complete markets
. 709
§
4c. Fundamental partial differential equation of hedge pricing
. 712
5. Arbitrage,
completeness, and hedge pricing in diffusion
models of bonds
. 717
§5a. Models without opportunities for arbitrage
. 717
§
5b. Completeness
. 728
§
5c. Fundamental partial differentai equation of the term structure
of bonds
. 730
Chapter
VIII.
Theory of Pricing in Stochastic Financial Models.
Continuous Time
734
1.
European options in diffusion (B, S^-stockmarkets
. 735
§
la. Bachelier's formula
. 735
§
lb. Black-Scholes formula. Martingale inference
. 739
§
lc. Black-Scholes formula. Inference based on the solution
of the fundamental equation
. 745
§
Id. Black-Scholes formula. Case with dividends
. 748
2.
American options in diffusion (B. 5)-stockmarkets.
Case of an infinite time horizon
. 751
§
2a. Standard call option
. 751
§
2b. Standard put option
. 763
§
2c. Combinations of put and call options
. 765
§
2d. Russian option
. 767
3.
American options in diffusion (B, 5')-stockmarkets.
Finite time horizons
. 778
§
3a. Special features of calculations on finite time intervals
. 778
§
3b. Optimal stopping problems and
Stephan
problems
. 782
§
3c.
Stephan
problem for standard call and put options
. 784
§ 3d.
Relations between the prices of European and American options
. 788
4.
European and American options in a diffusion
(B,'P)-bondmarket
. 792
§
4a. Option pricing in a bondmarket
. 792
§
4b. European option pricing in single-factor Gaussian models
. 795
§
4c. American option pricing in single-factor Gaussian models
. 799
Bibliography
. 803
Index
. 825
Index of symbols
. 833 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Širjaev, Alʹbert N. 1934- |
| author_GND | (DE-588)12203502X |
| author_facet | Širjaev, Alʹbert N. 1934- |
| author_role | aut |
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| author_variant | a n š an anš |
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| discipline | Mathematik Wirtschaftswissenschaften |
| discipline_str_mv | Mathematik Wirtschaftswissenschaften |
| edition | Repr. |
| format | Book |
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| id | DE-604.BV023292850 |
| illustrated | Illustrated |
| index_date | 2024-07-02T20:43:47Z |
| indexdate | 2024-07-09T21:15:08Z |
| institution | BVB |
| isbn | 9810236050 9789810236052 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016477433 |
| oclc_num | 254840656 |
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| physical | XVI, 834 S. graph. Darst. |
| publishDate | 2008 |
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| publisher | World Scientific |
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| series | Advanced series on statistical science & applied probability |
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| spelling | Širjaev, Alʹbert N. 1934- Verfasser (DE-588)12203502X aut Essentials of stochastic finance facts, models, theory Albert N. Shiryaev Repr. Singapore [u.a.] World Scientific 2008 XVI, 834 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Advanced series on statistical science & applied probability 3 Aus dem Russ. übers. Finanzmathematik - Stochastischer Prozess Stochastisches Modell - Kreditmarkt - Financial Engineering Stochastisches Modell (DE-588)4057633-4 gnd rswk-swf Finanzwirtschaft (DE-588)4017214-4 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Finanzmathematik (DE-588)4017195-4 gnd rswk-swf Stochastisches Modell (DE-588)4057633-4 s Finanzwirtschaft (DE-588)4017214-4 s DE-604 Finanzmathematik (DE-588)4017195-4 s Stochastischer Prozess (DE-588)4057630-9 s Advanced series on statistical science & applied probability 3 (DE-604)BV011932321 3 Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016477433&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Širjaev, Alʹbert N. 1934- Essentials of stochastic finance facts, models, theory Advanced series on statistical science & applied probability Finanzmathematik - Stochastischer Prozess Stochastisches Modell - Kreditmarkt - Financial Engineering Stochastisches Modell (DE-588)4057633-4 gnd Finanzwirtschaft (DE-588)4017214-4 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Finanzmathematik (DE-588)4017195-4 gnd |
| subject_GND | (DE-588)4057633-4 (DE-588)4017214-4 (DE-588)4057630-9 (DE-588)4017195-4 |
| title | Essentials of stochastic finance facts, models, theory |
| title_auth | Essentials of stochastic finance facts, models, theory |
| title_exact_search | Essentials of stochastic finance facts, models, theory |
| title_exact_search_txtP | Essentials of stochastic finance facts, models, theory |
| title_full | Essentials of stochastic finance facts, models, theory Albert N. Shiryaev |
| title_fullStr | Essentials of stochastic finance facts, models, theory Albert N. Shiryaev |
| title_full_unstemmed | Essentials of stochastic finance facts, models, theory Albert N. Shiryaev |
| title_short | Essentials of stochastic finance |
| title_sort | essentials of stochastic finance facts models theory |
| title_sub | facts, models, theory |
| topic | Finanzmathematik - Stochastischer Prozess Stochastisches Modell - Kreditmarkt - Financial Engineering Stochastisches Modell (DE-588)4057633-4 gnd Finanzwirtschaft (DE-588)4017214-4 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Finanzmathematik (DE-588)4017195-4 gnd |
| topic_facet | Finanzmathematik - Stochastischer Prozess Stochastisches Modell - Kreditmarkt - Financial Engineering Stochastisches Modell Finanzwirtschaft Stochastischer Prozess Finanzmathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016477433&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV011932321 |
| work_keys_str_mv | AT sirjaevalʹbertn essentialsofstochasticfinancefactsmodelstheory |