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Lévy Matters I: Recent Progress in Theory and Applications: Foundations, Trees and Numerical Issues in Finance 2010 ed. [Minkštas viršelis]

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  • Formatas: Paperback / softback, 206 pages, aukštis x plotis: 235x155 mm, weight: 413 g, XIV, 206 p., 1 Paperback / softback
  • Serija: Lecture Notes in Mathematics 2001
  • Išleidimo metai: 05-Sep-2010
  • Leidėjas: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • ISBN-10: 3642140068
  • ISBN-13: 9783642140068
Kitos knygos pagal šią temą:
Lévy Matters I: Recent Progress in Theory and Applications: Foundations, Trees and Numerical Issues in Finance 2010 ed.Didesnis paveikslėlis
  • Formatas: Paperback / softback, 206 pages, aukštis x plotis: 235x155 mm, weight: 413 g, XIV, 206 p., 1 Paperback / softback
  • Serija: Lecture Notes in Mathematics 2001
  • Išleidimo metai: 05-Sep-2010
  • Leidėjas: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • ISBN-10: 3642140068
  • ISBN-13: 9783642140068
Kitos knygos pagal šią temą:
Pastovi nuoroda: https://www.kriso.lt/db/9783642140068.html
Raktažodžiai:
This series reports on new developments in mathematical research and teaching-quickly, informally and at a high level.

Texts that are out of print but still in demand may also be considered.

The timeliness of a manuscript is sometimes more important than its form, which may in such cases be preliminary or tentative.

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Manuscripts should be prepared according to Springer-Verlag's standard specifications. Latex style files may be found at www.springer.com>Authors>Author Guidelines.

This is the first volume of a subseries of the Lecture Notes in Mathematics called Levy Matters, which will appear randomly over the next years. Each volume will describe some important topic in the theory or applications of Levy processes and pay tribute to the state of the art of this rapidly evolving subject with special emphasis on the non-Brownian world.

The three expository articles of this first volume have been chosen to reflect the breadth of the area of Levy processes. The first article by Ken-iti Sato characterizes extensions of the class of selfdecomposable distributions on Rd. The second article by Thomas Duquesne discusses Haudorff and packing measures of stable trees. The third article by Oleg Reichmann and Christoph Schwab presents numerical solutions to Kolmogoroff equations, which arise for instance in financial engineering, when Levy or additive processes model the dynamics of the risky assets.
Fractional Integrals and Extensions of Selfdecomposability
1(92)
Ken-Iti Sato
1 Introduction
2(9)
1.1 Characterizations of Selfdecomposable Distributions
2(2)
1.2 Nested Classes of Multiply Selfdecomposable Distributions
4(1)
1.3 Continuous-Parameter Extension of Multiple Selfdecomposability
4(1)
1.4 Stable Distributions and the Class L∞
5(1)
1.5 Fractional Integrals
6(2)
1.6 The Classes Kp,α and Lp,α Generated by Stochastic Integral Mappings
8(2)
1.7 Remarkable Subclasses of ID
10(1)
2 Fractional Integrals and Monotonicity of Order p>0
11(15)
2.1 Basic Properties
11(4)
2.2 One-to-One Property
15(4)
2.3 More Properites and Examples
19(7)
3 Preliminaries in Probability Theory
26(11)
3.1 Levy-Khintchine Representation of Infinitely Divisible Distributions
26(1)
3.2 Radial and Spherical Decompositions of σ-Finite Measures on Rd
27(2)
3.3 Weak Mean of Infinitely Divisible Distributions
29(2)
3.4 Stochastic Integral Mappings of Infinitely Divisible Distributions
31(5)
3.5 Transformation of Levy Measures
36(1)
4 First Two-Parameter Extension Kp, a of the Class L of Selfdecomposable Distributions
37(20)
4.1 Φf and ΦL/f for f = φα
37(4)
4.2 Φp,α and ΦL/P,α
41(4)
4.3 Range of ΦL/P,α
45(2)
4.4 Classes Kp,α, Ko/p,α, and Ke/p,α
47(10)
5 One-Parameter Subfamilies of {Kp,α}
57(11)
5.1 Kp,α, KO/p,α' and Ke/p,α for pε(0,∞) with Fixed α
57(8)
5.2 Kp,α, Ko/p,α, and Ke/p,α for αε(-∞, 2) with Fixed p
65(3)
6 Second Two-Parameter Extension Lp,α of the Class L of Selfdecomposable Distributions
68(10)
6.1 Ap,α and AL/P,α
68(5)
6.2 Range of AL/P,α
73(1)
6.3 Classes Lp,α, Lo/p,α' and Lep,α
74(3)
6.4 Relation Between Kp,α and Lp,α
77(1)
7 One-Parameter Subfamilies of {Lp,α}
78(11)
7.1 Lp,α, Lo/p,α and Le/p,α for pε(0,∞) with fixed α
78(9)
7.2 Lp,α, Lo/p,α, and Lep,α for αε(-∞, 2) with Fixed p
87(2)
References
89(4)
Packing and Hausdorff Measures of Stable Trees
93(44)
Thomas Duquesne
1 Introduction
93(9)
2 Notation, Definitions and Preliminary Results
102(15)
2.1 Hausdorff and Packing Measures on Metric Spaces
102(1)
2.2 Height Processes and Levy Trees
103(10)
2.3 Estimates
113(4)
3 Proofs of the Main Results
117(18)
3.1 Proof of Theorem 1.1
117(4)
3.2 Proof of Proposition 1.5
121(1)
3.3 Proof of Proposition 1.9
122(1)
3.4 Proof of Theorems 1.6 and 1.10
123(12)
References
135(2)
Numerical Analysis of Additive, Levy and Feller Processes with Applications to Option Pricing
137(60)
Oleg Reichmann
Christoph Schwab
1 Introduction
138(2)
2 Markov Processes
140(5)
2.1 Time-Homogeneous Processes
140(4)
2.2 Time-Inhomogeneous Processes
144(1)
3 Function Spaces
145(3)
4 Multivariate Model Setting
148(8)
4.1 Copula Functions
148(3)
4.2 Sector Condition
151(3)
4.3 A Class of Admissible Market Models
154(2)
5 Variational PIDE Formulations
156(12)
5.1 European Options
157(3)
5.2 American Options
160(4)
5.3 Greeks
164(4)
6 Wavelets
168(10)
6.1 Spline Wavelets on an Interval
169(4)
6.2 Tensor Product Spaces
173(1)
6.3 Space Discretization
174(3)
6.4 Wavelet Compression
177(1)
7 Computational Scheme
178(3)
7.1 Time Discretization
178(1)
7.2 Numerical Quadratures
179(2)
8 Alternative Pricing Approaches
181(4)
8.1 Monte Carlo Simulation
181(2)
8.2 Fourier Pricing
183(2)
9 Numerical Examples
185(7)
9.1 Univariate Case
186(4)
9.2 Multidimensional Case
190(2)
List of Symbols
192(1)
References
193(4)
Index 197