Atnaujinkite slapukų nuostatas

El. knyga: Stochastic Processes: From Applications to Theory [Taylor & Francis e-book]

(University of New South Wales, Sydney, Australia), (School of Mathematics and Statistics University of New South Wales; Sydney Australia & INRIA Bordeaux-Sud Ouest Research Center, France)
Kitos knygos pagal šią temą:
  • Taylor & Francis e-book
  • Kaina: 180,03 €*
  • * this price gives unlimited concurrent access for unlimited time
  • Standartinė kaina: 257,19 €
  • Sutaupote 30%
Stochastic Processes: From Applications to TheoryDidesnis paveikslėlis
Kitos knygos pagal šią temą:
Taylor & Francis e-booksMore info about Taylor & Francis e-books
Partnerių interneto svetainė: https://www.taylorfrancis.com/books/9781315381619

Unlike traditional books presenting stochastic processes in an academic way, this book includes concrete applications that students will find interesting such as gambling, finance, physics, signal processing, statistics, fractals, and biology. Written with an important illustrated guide in the beginning, it contains many illustrations, photos and pictures, along with several website links. Computational tools such as simulation and Monte Carlo methods are included as well as complete toolboxes for both traditional and new computational techniques.

Introduction xxi
I An illustrated guide
1(68)
1 Motivating examples
3(22)
1.1 Lost in the Great Sloan Wall
3(3)
1.2 Meeting Alice in Wonderland
6(1)
1.3 The lucky MIT Blackjack Team
7(3)
1.4 Kruskal's magic trap card
10(2)
1.5 The magic fern from Daisetsuzan
12(3)
1.6 The Kepler-22b Eve
15(2)
1.7 Poisson's typos
17(4)
1.8 Exercises
21(4)
2 Selected topics
25(18)
2.1 Stabilizing populations ...
25(3)
2.2 The traps of reinforcement
28(3)
2.3 Casino roulette
31(3)
2.4 Surfing Google's waves
34(2)
2.5 Pinging hackers
36(1)
2.6 Exercises
37(6)
3 Computational and theoretical aspects
43(26)
3.1 From Monte Carlo to Los Alamos
43(2)
3.2 Signal processing and population dynamics
45(4)
3.3 The lost equation
49(7)
3.4 Towards a general theory
56(4)
3.5 The theory of speculation
60(6)
3.6 Exercises
66(3)
II Stochastic simulation
69(50)
4 Simulation toolbox
71(6)
4.1 Inversion technique
71(3)
4.2 Change of variables
74(1)
4.3 Rejection techniques
75(2)
44 Sampling probabilities
77(22)
4.4.1 Bayesian inference
77(2)
4.4.2 Laplace's rule of successions
79(1)
4.4.3 Fragmentation and coagulation
79(1)
4.5 Conditional probabilities
80(5)
4.5.1 Bayes' formula
80(1)
4.5.2 The regression formula
81(1)
4.5.3 Gaussian updates
82(2)
4.5.4 Conjugate priors
84(1)
4.6 Spatial Poisson point processes
85(7)
4.6.1 Some preliminary results
85(3)
4.6.2 Conditioning principles
88(3)
4.6.3 Poisson-Gaussian clusters
91(1)
4.7 Exercises
92(7)
5 Monte Carlo integration
99(8)
5.1 Law of large numbers
99(3)
5.2 Importance sampling
102(2)
5.2.1 Twisted distributions
102(1)
5.2.2 Sequential Monte Carlo
102(1)
5.2.3 Tails distributions
103(1)
5.3 Exercises
104(3)
6 Some illustrations
107(12)
6.1 Stochastic processes
107(1)
6.2 Markov chain models
108(1)
6.3 Black-box type models
108(2)
6.4 Boltzmann-Gibbs measures
110(3)
6.4.1 Ising model
110(1)
6.4.2 Sherrington-Kirkpatrick model
111(1)
6.4.3 The traveling salesman model
111(2)
6.5 Filtering and statistical learning
113(2)
6.5.1 Bayes' formula
113(1)
6.5.2 Singer's radar model
114(1)
6.6 Exercises
115(4)
III Discrete time processes
119(178)
7 Markov chains
121(20)
7.1 Description of the models
121(1)
7.2 Elementary transitions
122(1)
7.3 Markov integral operators
123(1)
7.4 Equilibrium measures
124(1)
7.5 Stochastic matrices
125(1)
7.6 Random dynamical systems
126(2)
7.6.1 Linear Markov chain model
126(1)
7.6.2 Two-states Markov models
127(1)
7.7 Transition diagrams
128(1)
7.8 The tree of outcomes
128(1)
7.9 General state space models
129(3)
7.10 Nonlinear Markov chains
132(6)
7.10.1 Self interacting processes
132(2)
7.10.2 Mean field particle models
134(1)
7.10.3 McKean-Vlasov diffusions
135(1)
7.10.4 Interacting jump processes
136(2)
7.11 Exercises
138(3)
8 Analysis toolbox
141(80)
8.1 Linear algebra
141(4)
8.1.1 Diagonalisation type techniques
141(2)
8.1.2 Perron Frobenius theorem
143(2)
8.2 Functional analysis
145(21)
8.2.1 Spectral decompositions
145(4)
8.2.2 Total variation norms
149(3)
8.2.3 Contraction inequalities
152(4)
8.2.4 Poisson equation
156(1)
8.2.5 V-norms
156(4)
8.2.0 Geometric drift conditions
160(4)
8.2.7 V-norm contractions
164(2)
8.3 Stochastic analysis
166(12)
8.3.1 Coupling techniques
166(1)
8.3.1.1 The total variation distance
166(3)
8.3.1.2 Wasserstein metric
169(3)
8.3.2 Stopping times and coupling
172(1)
8.3.3 Strong stationary times
173(1)
8.3.4 Some illustrations
174(1)
8.3.4.1 Minorization condition and coupling
174(2)
8.3.4.2 Markov chains on complete graphs
176(1)
8.3.4.3 A Kruskal random walk
177(1)
8.4 Martingales
178(25)
8.4.1 Some preliminaries
178(5)
8.4.2 Applications to Markov chains
183(1)
8.4.2.1 Martingales with fixed terminal values
183(1)
8.4.2.2 Doeblin-Ito formula
184(1)
8.4.2.3 Occupation measures
185(2)
8.4.3 Optional stopping theorems
187(4)
8.4.4 A gambling model
191(1)
8.4.4.1 Fair games
192(1)
8.4.4.2 Unfair games
193(1)
8.4.5 Maximal inequalities
194(2)
8.4.6 Limit theorems
196(7)
8.5 Topological aspects
203(9)
8.5.1 Irreducibility and aperiodicity
203(3)
8.5.2 Recurrent and transient states
206(4)
8.5.3 Continuous state spaces
210(1)
8.5.4 Path space models
211(1)
8.6 Exercises
212(9)
9 Computational toolbox
221(76)
9.1 A weak ergodic theorem
221(3)
9.2 Some illustrations
224(2)
9.2.1 Parameter estimation
224(1)
9.2.2 Gaussian subset shaker
225(1)
9.2.3 Exploration of the unit disk
226(1)
9.3 Markov Chain Monte Carlo methods
226(10)
9.3.1 Introduction
226(1)
9.3.2 Metropolis and Hastings models
227(2)
9.3.3 Gibbs-Glauber dynamics
229(4)
9.3.4 Propp and Wilson sampler
233(3)
9.4 Time inhoinogeneous MCMC models
236(3)
9.4.1 Simulated annealing algorithm
236(1)
9.4.2 A perfect sampling algorithm
237(2)
9.5 Feynman-Kac path integration
239(13)
9.5.1 Weighted Markov chains
239(1)
9.5.2 Evolution equations
240(2)
9.5.3 Particle absorption models
242(2)
9.5.4 Doob h-processes
244(1)
9.5.5 Quasi-invariant measures
245(2)
9.5.6 Cauchy problems with terminal conditions
247(1)
9.5.7 Dirichlet-Poisson problems
248(2)
9.5.8 Cauchy-Dirichlet-Poisson problems
250(2)
9.6 Feynman-Kac particle methodology
252(8)
9.6.1 Mean field genetic type particle models
252(2)
9.6.2 Path space models
254(1)
9.6.3 Backward integration
255(2)
9.6.4 A random particle matrix model
257(1)
9.6.5 A conditional formula for ancestral trees
258(2)
9.7 Particle Markov chain Monte Carlo methods
260(7)
9.7.1 Many-body Feynman-Kac measures
260(1)
9.7.2 A particle Metropolis-Hastings model
261(1)
9.7.3 Duality formulae for many-body models
262(4)
9.7.4 A couple particle Gibbs samplers
266(1)
9.8 Quenched and annealed measures
267(5)
9.8.1 Feynman-Kac models
267(2)
9.8.2 Particle Gibbs models
269(2)
9.8.3 Particle Metropolis-Hastings models
271(1)
9.9 Some application domains
272(14)
9.9.1 Interacting MCMC algorithms
272(4)
9.9.2 Nonlinear filtering models
276(1)
9.9.3 Markov chain restrictions
276(1)
9.9.4 Self avoiding walks
277(2)
9.9.5 Twisted measure importance sampling
279(1)
9.9.6 Kalman-Bucy filters
280(1)
9.9.6.1 Forward filters
280(1)
9.9.6.2 Backward filters
281(2)
9.9.6.3 Ensemble Kaiman filters
283(2)
9.9.6.4 Interacting Kaiman filters
285(1)
9.10 Exercises
286(11)
IV Continuous time processes
297(236)
10 Poisson processes
299(14)
10.1 A counting process
299(1)
10.2 Memoryless property
300(1)
10.3 Uniform random times
301(1)
10.4 Doeblin-Ito formula
302(2)
10.5 Bernoulli process
304(2)
10.6 Time inhomogeneous models
306(5)
10.6.1 Description of the models
306(3)
10.6.2 Poisson thinning simulation
309(1)
10.6.3 Geometric random clocks
309(2)
10.7 Exercises
311(2)
11 Markov chain embeddings
313(24)
11.1 Homogeneous embeddings
313(4)
11.1.1 Description of the models
313(1)
11.1.2 Semigroup evolution equations
314(3)
11.2 Some illustrations
317(5)
11.2.1 A two-state Markov process
317(1)
11.2.2 Matrix valued equations
318(2)
11.2.3 Discrete Laplacian
320(2)
11.3 Spatially inhomogeneous models
322(7)
11.3.1 Explosion phenomenon
324(4)
11.3.2 Finite state space models
328(1)
11.4 Time inhomogeneous models
329(3)
11.4.1 Description of the models
329(2)
11.4.2 Poisson thinning models
331(1)
11.4.3 Exponential and geometric clocks
332(1)
11.5 Exercises
332(5)
12 Jump processes
337(26)
12.1 A class of pure jump models
337(1)
12.2 Semigroup evolution equations
338(2)
12.3 Approximation schemes
340(2)
12.4 Sum of generators
342(2)
12.5 Doob-Meyer decompositions
344(6)
12.5.1 Discrete time models
344(2)
12.5.2 Continuous time martingales
346(3)
12.5.3 Optional stopping theorems
349(1)
12.6 Doeblin-Ito-Taylor formulae
350(1)
12.7 Stability properties
351(5)
12.7.1 Invariant measures
351(2)
12.7.2 Dobrushin contraction properties
353(3)
12.8 Exercises
356(7)
13 Piecewise deterministic processes
363(30)
13.1 Dynamical systems basics
363(4)
13.1.1 Semigroup and flow maps
363(3)
13.1.2 Time discretization schemes
366(1)
13.2 Piecewise deterministic jump models
367(10)
13.2.1 Excursion valued Markov chains
367(2)
13.2.2 Evolution semigroups
369(2)
13.2.3 Infinitesimal generators
371(1)
13.2.4 Fokker-Planck equation
372(1)
13.2.5 A time discretization scheme
373(3)
13.2.6 Doeblin-Ito-Taylor formulae
376(1)
13.3 Stability properties
377(2)
13.3.1 Switching processes
377(2)
13.3.2 Invariant measures
379(1)
13.4 An application to Internet architectures
379(5)
13.4.1 The transmission control protocol
379(2)
13.4.2 Regularity and stability properties
381(2)
13.4.3 The limiting distribution
383(1)
13.5 Exercises
384(9)
14 Diffusion processes
393(32)
14.1 Brownian motion
393(8)
14.1.1 Discrete vs continuous time models
393(2)
14.1.2 Evolution semigroups
395(2)
14.1.3 The heat equation
397(1)
14.1.4 Doeblin-Ito-Taylor formula
398(3)
14.2 Stochastic differential equations
401(4)
14.2.1 Diffusion processes
401(1)
14.2.2 Doeblin-Ito differential calculus
402(3)
14.3 Evolution equations
405(4)
14.3.1 Fokker-Planck equation
405(1)
11.3.2 Weak approximation processes
406(2)
11.3.3 A backward stochastic differential equation
408(1)
14.4 Multidimensional diffusions
409(4)
14.4.1 Multidimensional stochastic differential equations
409(2)
14.4.2 An integration by parts formula
411(1)
14.1.3 Laplacian and orthogonal transformations
412(1)
14.4.4 Fokker-Planck equation
413(1)
14.5 Exercises
413(12)
15 Jump diffusion processes
425(38)
15.1 Piecewise diffusion processes
425(1)
15.2 Evolution semigroups
426(2)
15.3 Doeblin-Ito formula
428(5)
15.4 Fokker-Planck equation
433(1)
15.5 An abstract class of stochastic processes
434(5)
15.5.1 Generators and carre du champ operators
434(3)
15.5.2 Perturbation formulae
437(2)
15.6 Jump diffusion processes with killing
439(11)
15.6.1 Feymnan-Kac semigroups
439(1)
15.6.2 Cauchy problems with terminal conditions
440(2)
15.6.3 Dirichlet-Poisson problems
442(5)
15.6.4 Cauchy-Dirichlet-Poisson problems
447(3)
15.7 Some illustrations
450(1)
15.7.1 One-dimensional Dirichlet-Poisson problems
450(1)
15.7.2 A backward stochastic differential equation
451(1)
15.8 Exercises
451(12)
16 Nonlinear jump diffusion processes
463(18)
16.1 Nonlinear Markov processes
463(5)
16.1.1 Pure diffusion models
463(1)
16.1.2 Burgers equation
464(2)
16.1.3 Feymnan-Kac jump type models
466(1)
16.1.4 A jump type Langevin model
467(1)
16.2 Mean field particle models
468(2)
16.3 Some application domains
470(4)
16.3.1 Fouque-Sun systemic risk model
470(1)
16.3.2 Burgers equation
471(1)
16.3.3 Langevin-McKean-Vlasov model
472(1)
16.3.4 Dyson equation
473(1)
16.4 Exercises
474(7)
17 Stochastic analysis toolbox
481(20)
17.1 Time changes
481(1)
17.2 Stability properties
482(1)
17.3 Some illustrations
483(2)
17.3.1 Gradient flow processes
483(1)
17.3.2 One-dimensional diffusions
484(1)
17.4 Foster-Lyapunov techniques
485(2)
17.4.1 Contraction inequalities
485(1)
17.4.2 Minorization properties
486(1)
17.5 Some applications
487(3)
17.5.1 Ornstein-Uhlenbeck processes
487(1)
17.5.2 Stochastic gradient processes
487(1)
17.5.3 Langevin diffusions
488(2)
17.6 Spectral analysis
490(5)
17.6.1 Hilbert spaces and Schauder bases
490(3)
17.6.2 Spectral decompositions
493(1)
17.6.3 Poincare inequality
494(1)
17.7 Exercises
495(6)
18 Path space measures
501(32)
18.1 Pure jump models
501(6)
18.1.1 Likelihood functionals
504(1)
18.1.2 Girsanov's transformations
505(1)
18.1.3 Exponential martingales
506(1)
18.2 Diffusion models
507(5)
18.2.1 Wiener measure
507(1)
18.2.2 Path space diffusions
508(1)
18.2.3 Girsanov transformations
509(3)
18.3 Exponential change twisted measures
512(2)
18.3.1 Diffusion processes
513(1)
18.3.2 Pure jump processes
514(1)
18.4 Some illustrations
514(3)
18.4.1 Risk neutral financial markets
514(1)
18.4.1.1 Poisson markets
514(1)
18.4.1.2 Diffusion markets
515(1)
18.4.2 Elliptic diffusions
516(1)
18.5 Nonlinear filtering
517(10)
18.5.1 Diffusion observations
517(1)
18.5.2 Dunean-Zakai equation
518(2)
18.5.3 Kushner-Stratonovitch equation
520(1)
18.5.4 Kalman-Bucy filters
521(2)
18.5.5 Nonlinear diffusion and ensemble Kalman-Bucy filters
523(1)
18.5.0 Robust filtering equations
524(1)
18.5.7 Poisson observations
525(2)
18.6 Exercises
527(6)
V Processes on manifolds
533(158)
19 A review of differential geometry
535(44)
19.1 Projection operators
535(6)
19.2 Covariant derivatives of vector fields
541(6)
19.2.1 First order derivatives
543(3)
19.2.2 Second order derivatives
546(1)
19.3 Divergence and mean curvature
547(7)
19.4 Lie brackets and commutation formulae
554(2)
19.5 Inner product derivation formulae
556(3)
19.6 Second order derivatives and some trace formulae
559(3)
19.7 Laplacian operator
562(1)
19.8 Ricci curvature
563(5)
19.9 Bochner-Lichnerowicz formula
568(8)
19.10 Exercises
576(3)
20 Stochastic differential calculus on manifolds
579(14)
20.1 Embedded manifolds
579(2)
20.2 Brownian motion on manifolds
581(3)
20.2.1 A diffusion model in the ambient space
581(2)
20.2.2 The infinitesimal generator
583(1)
20.2.3 Monte Carlo simulation
584(1)
20.3 Stratonovitch differential calculus
584(2)
20.4 Projected diffusions on manifolds
586(3)
20.5 Brownian motion on orbifolds
589(2)
20.6 Exercises
591(2)
21 Parametrizations and charts
593(36)
21.1 Differentiable manifolds and charts
593(3)
21.2 Orthogonal projection operators
596(3)
21.3 Riemannian structures
599(3)
21.4 First order covariant derivatives
602(7)
21.4.1 Pushed forward functions
602(2)
21.4.2 Pushed forward vector fields
604(2)
21.4.3 Directional derivatives
606(3)
21.5 Second order covariant derivative
609(8)
21.5.1 Tangent basis functions
609(3)
21.5.2 Composition formulae
612(1)
21.5.3 Hessian operators
613(4)
21.6 Bochner-Lichnerowicz formula
617(6)
21.7 Exercises
623(6)
22 Stochastic calculus in chart spaces
629(10)
22.1 Brownian motion on Riemannian manifolds
629(2)
22.2 Diffusions on chart spaces
631(1)
22.3 Brownian motion on spheres
632(2)
22.3.1 The unit circle S = S1 ⊂ R1
632(1)
22.3.2 The unit sphere S = S2 ⊂ R2
633(1)
22.4 Brownian motion on the torus
634(1)
22.5 Diffusions on the simplex
635(2)
22.6 Exercises
637(2)
23 Some analytical aspects
639(34)
23.1 Geodesics and the exponential map
639(4)
23.2 Taylor expansion
643(2)
23.3 Integration on manifolds
645(12)
23.3.1 The volume measure on the manifold
645(3)
23.3.2 Wedge product and volume forms
648(2)
23.3.3 The divergence theorem
650(7)
23.4 Gradient flow models
657(2)
23.4.1 Steepest descent model
657(1)
23.4.2 Euclidian state spaces
658(1)
23.5 Drift changes and irreversible Langevin diffusions
659(6)
23.5.1 Langevin diffusions on closed manifolds
661(1)
23.5.2 Riemannian Langevin diffusions
662(3)
23.6 Metropolis-adjusted Langevin models
665(1)
23.7 Stability and some functional inequalities
666(3)
23.8 Exercises
669(4)
24 Some illustrations
673(18)
24.1 Prototype manifolds
673(8)
24.1.1 The circle
673(1)
24.1.2 The 2-sphere
674(4)
24.1.3 The torus
678(3)
24.2 Information theory
681(10)
24.2.1 Nash embedding theorem
681(1)
24.2.2 Distribution manifolds
682(1)
24.2.3 Bayesian statistical manifolds
683(2)
24.2.4 Cramer-Rao lower bound
685(1)
24.2.5 Some illustrations
685(1)
24.2.5.1 Boltzmann-Gibbs measures
685(1)
24.2.5.2 Multivariate normal distributions
686(5)
VI Some application areas
691(148)
25 Simple random walks
693(12)
25.1 Random walk on lattices
693(1)
25.1.1 Description
693(1)
25.1.2 Dimension 1
693(1)
25.1.3 Dimension 2
694(1)
25.1.4 Dimension d ≥ 3
694(1)
25.2 Random walks on graphs
694(1)
25.3 Simple exclusion process
695(1)
25.4 Random walks on the circle
695(2)
25.4.1 Markov chain on cycle
695(1)
25.4.2 Markov chain on circle
696(1)
25.4.3 Spectral decomposition
696(1)
25.5 Random walk on hypercubes
697(2)
25.5.1 Description
697(1)
25.5.2 A macroscopic model
698(1)
25.5.3 A lazy random walk
698(1)
25.6 Urn processes
699(2)
25.6.1 Ehrenfest model
699(1)
25.6.2 Polya urn model
700(1)
25.7 Exercises
701(4)
26 Iterated random functions
705(26)
26.1 Description
705(2)
26.2 A motivating example
707(1)
26.3 Uniform selection
708(4)
26.3.1 An ancestral type evolution model
708(1)
26.3.2 An absorbed Markov chain
709(3)
26.4 Shuffling cards
712(7)
26.4.1 Introduction
712(1)
26.4.2 The top-in-at-random shuffle
712(1)
26.4.3 The random transposition shuffle
713(3)
26.4.4 The riffle shuffle
716(3)
26.5 Fractal models
719(6)
26.5.1 Exploration of Cantor's discontinuum
720(3)
26.5.2 Some fractal images
723(2)
26.6 Exercises
725(6)
27 Computational and statistical physics
731(28)
27.1 Molecular dynamics simulation
731(6)
27.1.1 Newton's second law of motion
731(3)
27.1.2 Langevin diffusion processes
734(3)
27.2 Schrodinger equation
737(12)
27.2.1 A physical derivation
737(2)
27.2.2 Feynman-Kac formulation
739(3)
27.2.3 Bra-kets and path integral formalism
742(1)
27.2.4 Spectral decompositions
743(2)
27.2.5 The harmonic oscillator
745(3)
27.2.6 Diffusion Monte Carlo models
748(1)
27.3 Interacting particle systems
749(4)
27.3.1 Introduction
749(2)
27.3.2 Contact process
751(1)
27.3.3 Voter process
751(1)
27.3.4 Exclusion process
752(1)
27.4 Exercises
753(6)
28 Dynamic population models
759(28)
28.1 Discrete time birth and death models
759(3)
28.2 Continuous time models
762(7)
28.2.1 Birth and death generators
762(1)
28.2.2 Logistic processes
762(2)
28.2.3 Epidemic model with immunity
764(1)
28.2.4 Lotka-Volterra predator-prey stochastic model
765(3)
28.2.5 Moran genetic model
768(1)
28.3 Genetic evolution models
769(1)
28.4 Branching processes
770(10)
28.4.1 Birth and death models with linear rates
770(2)
28.4.2 Discrete time branching processes
772(1)
28.4.3 Continuous time branching processes
773(1)
28.4.3.1 Absorption-death process
774(1)
28.4.3.2 Birth type branching process
775(2)
28.4.3.3 Birth and death branching processes
777(1)
28.4.3.4 Kolmogorov-Petrovskii-Piskunov equation
778(2)
28.5 Exercises
780(7)
29 Gambling, ranking and control
787(34)
29.1 Google page rank
787(1)
29.2 Gambling betting systems
788(9)
29.2.1 Martingale systems
788(1)
29.2.2 St. Petersburg martingales
789(2)
29.2.3 Conditional gains and losses
791(1)
29.2.3.1 Conditional gains
791(1)
29.2.3.2 Conditional losses
791(1)
29.2.4 Bankroll management
792(2)
29.2.5 Grand martingale
794(1)
29.2.6 D'Alembert martingale
794(2)
29.2.7 Whittacker martingale
796(1)
29.3 Stochastic optimal control
797(10)
29.3.1 Bellman equations
797(5)
29.3.2 Control dependent value functions
802(2)
29.3.3 Continuous time models
804(3)
29.4 Optimal stopping
807(5)
29.4.1 Games with fixed terminal condition
807(2)
29.4.2 Snell envelope
809(2)
29.4.3 Continuous time models
811(1)
29.5 Exercises
812(9)
30 Mathematical finance
821(18)
30.1 Stock price models
821(5)
30.1.1 Up and down martingales
821(3)
30.1.2 Cox-Ross-Rubinstein model
824(1)
30.1.3 Black-Scholes-Merton model
825(1)
30.2 European option pricing
826(9)
30.2.1 Call and put options
826(1)
30.2.2 Self-financing portfolios
827(1)
30.2.3 Binomial pricing technique
828(2)
30.2.4 Black-Scholes-Merton pricing model
830(1)
30.2.5 Black-Scholes partial differential equation
831(1)
30.2.6 Replicating portfolios
832(1)
30.2.7 Option price and hedging computations
833(1)
30.2.8 A numerical illustration
834(1)
30.3 Exercises
835(4)
Bibliography 839(16)
Index 855
Pierre Del Moral and Spiridon Penev are professors in the School of Mathematics and Statistics at the University of New South Wales.
Pastovi nuoroda: https://www.kriso.lt/db/9781315381619_pe.html
Raktažodžiai: