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1.

図書
図書
1. Lévy processes
Jean Bertoin
出版情報: Cambridge [Eng.] : Cambridge University Press, 1996  x, 265 p. ; 24 cm
シリーズ名: Cambridge tracts in mathematics ; 121
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2.

図書
図書
2. Malliavin calculus for Lévy processes and infinite-dimensional Brownian motion : an introduction
Horst Osswald
出版情報: Cambridge : Cambridge University Press, 2012  xix, 407 p. ; 24 cm
シリーズ名: Cambridge tracts in mathematics ; 191
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目次情報: 続きを見る
The Fundamental Principles / Part I：
Preface / 1：
Martingales / 2：
Fourier and Laplace transformations / 3：
Abstract Wiener-Fréchet spaces / 4：
Two concepts of no-anticipation in time / 5：
Malliavin calculus on the space of real sequences / 6：
Introduction to poly-saturated models of mathematics / 7：
Extension of the real numbers and properties / 8：
Topology / 9：
Measure and integration on Loeb spaces / 10：
An Introduction to Finite- and Infinite-Dimensional Stochastic Analysis / Part II：
From finite- to infinite-dimensional Brownian motion / 11：
The Itô integral for infinite-dimensional Brownian motion / 12：
The iterated integral / 13：
Infinite-dimensional Ornstein-Uhlenbeck processes / 14：
Lindstrøm's construction of standard Lévy processes from discrete ones / 15：
Stochastic integration for Lévy processes / 16：
Malliavin Calculus / Part III：
Chaos decomposition / 17：
The Malliavin derivative / 18：
The Skorokhod integral / 19：
The interplay between derivative and integral / 20：
Skorokhod integral processes / 21：
Girsanov transformation / 22：
Malliavin calculus for Lévy processes / 23：
Poly-saturated models / Appendix A：
The existence of poly-saturated models / Appendix B：
References
Index
The Fundamental Principles / Part I：
Preface / 1：
Martingales / 2：
3.

図書
図書
3. Lévy processes : theory and applications (: Boston ; : Basel)
Ole E. Barndorff-Nielsen, Thomas Mikosch, Sidney I. Resnick, editors
出版情報: Boston : Birkhäuser, c2001  x, 415 p. ; 26 cm
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目次情報: 続きを見る
Preface
A tutorial on L+¼vy processes / Sato, KI：
Basic results on L+¼vy processes
Distributional, pathwise and structural results / Carmona, P ; Petit, F ; Yor, MII：
Exponentials functionals of Levy processes / Doney, R
Fluctuation theory for Levy processes / Marcus, M.B ; Rosen, J
Gaussian processes and the local times of symmetric L+¼vy processes / Watanabe, T
Temporal change in distributional properties of L+¼vy processes
Extensions and generalisations of L+¼vy processes / III：
Applebaum, D.: L+¼vy processes in stochastic differential geometry / Jac ; Schilling, R.L
L+¼vy-type processes and pseudo-differential operators / Maejima, M
Semi-stable distributions
Applications in physics / Albeverio, S ; R++diger, B ; Wu, J-LIV：
Analytic and probabilistic aspects of L+¼vy processes and fields in quantum theory / Holevo, A.S
L+¼vy processes and continuous quantum measurements / Woyczynski, W.A
L+¼vy processes in the physical sciences / Bertoin, J
Some properties of Burgers turbulence with white or stable noise
Applications in finance / Barndorff-Nielsen, O.E ; Shepard, NV：
Modelling by L+¼vy processes for financial econometrics / Eberlein, E
Application of generalized hyperbolic L+¼vy motions to finance / Ma, J ; Protter, P ; Zhang, J
Explicit form and path regularity of martingale representation
Interpretations in terms of Brownian and Bessel meanders of the distribution of a subordinated perpetuity
Numerical and statistical aspects / Nolan, J.PVI：
Maximum likelihood estimation and diagnostics for stable distributions / Rosinski, J
Series representations of L+¼vy processes from the perspective of point processes
Preface
A tutorial on L+¼vy processes / Sato, KI：
Basic results on L+¼vy processes
4.

図書
図書
4. The Lévy Laplacian
M.N. Feller
出版情報: Cambridge, UK ; New York : Cambridge University Press, 2005  vi, 153 p. ; 24 cm
シリーズ名: Cambridge tracts in mathematics ; 166
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Introduction
The Lévy Laplacian / 1：
Lévy-Laplace operators / 2：
Symmetric Lévy-Laplace operators / 3：
Harmonic functions of infinitely many variables / 4：
Linear elliptic and parabolic equations with Lévy Laplacians / 5：
Quasilinear and nonlinear elliptic equation with Lévy Laplacians / 6：
Nonlinear parabolic equations with Lévy Laplacians / 7：
Appendix. LévyâÇôDirichlet forms and associated Markov processes / 8：
Bibliography
Index
Introduction
The Lévy Laplacian / 1：
Lévy-Laplace operators / 2：
5.

図書
図書
5. Lévy processes and stochastic calculus (: hbk)
David Applebaum
出版情報: Cambridge : Cambridge University Press, 2004  xxiv, 384 p. ; 24 cm
シリーズ名: Cambridge studies in advanced mathematics ; 93
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Introduction / 1：
Levy processes / 2：
Martingales, stopping times and random measures / 3：
Markov processes, semigroups and generators / 4：
Stochastic integration / 5：
Exponential martingales, change of measure and financial applications / 6：
Stochastic differential equations / 7：
Notation
Bibliography
Index
Introduction / 1：
Levy processes / 2：
Martingales, stopping times and random measures / 3：
6.

図書
図書
6. Lévy processes in Lie groups
Ming Liao
出版情報: Cambridge : Cambridge University Press, 2004  x, 266 p. ; 24 cm
シリーズ名: Cambridge tracts in mathematics ; 162
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7.

図書
図書
7. Lévy processes and infinitely divisible distributions (: hardback)
Ken-iti Sato
出版情報: Cambridge : Cambridge University Press, 1999  xii, 486 p. ; 24 cm
シリーズ名: Cambridge studies in advanced mathematics ; 68
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目次情報: 続きを見る
Preface
Remarks on notation
Basic examples / 1：
Characterization and existence of Lèvy and additive processes / 2：
Stable processes and their extensions / 3：
The Lèvy-Ito decomposition of sample functions / 4：
Distributional properties of Lèvy processes / 5：
Subordination and density transformation / 6：
Recurrence and transience / 7：
Potential theory for Lèvy processes / 8：
Wiener-Hopf factorizations / 9：
More distributional properties / 10：
Solutions to exercises
References and author index
Subject index
Preface
Remarks on notation
Basic examples / 1：
8.

図書
図書
8. Malliavin calculus for Lévy processes with applications to finance. Corr. 2nd print
Giulia Di Nunno, Bernt Øksendal, Frank Proske
出版情報: Heidelberg : Springer, c2009  xiii, 417 p. ; 24 cm
シリーズ名: Universitext
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Introduction
The Continuous Case: Brownian Motion / Part I：
The Wiene-Ito Chaos Expansion / 1：
Iterated Ito Integrals / 1.1：
The Wiener-Ito Chaos Expansion / 1.2：
Exercises / 1.3：
The Skorohod Integral / 2：
Some Basic Properties of the Skorohod Integral / 2.1：
The Skorohod Integral as an Extension of the Ito Integral / 2.3：
Malliavin Derivative via Chaos Expansion / 2.4：
The Malliavin Derivative / 3.1：
Computation and Properties of the Malliavin Derivative / 3.2：
Chain Rules for Malliavin Derivative / 3.2.1：
Malliavin Derivative and Conditional Expectation / 3.2.2：
Malliavin Derivative and Skorohod Integral / 3.3：
Skorohod Integral as Adjoint Operator to the Malliavin Derivative / 3.3.1：
An Integration by Parts Formula and Closability of the Skorohod Integral / 3.3.2：
A Fundamental Theorem of Calculus / 3.3.3：
Integral Representations and the Clark-Ocone Formula / 3.4：
The Clark-Ocone Formula / 4.1：
The Clark-Ocone Formula under Change of Measure / 4.2：
Application to Finance: Portfolio Selection / 4.3：
Application to Sensitivity Analysis and Computation of the "Greeks" in Finance / 4.4：
White Noise, the Wick Product, and Stochastic Integration / 4.5：
White Noise Probability Space / 5.1：
The Wiener-Ito Chaos Expansion Revisited / 5.2：
The Wick Product and the Hermite Transform / 5.3：
Some Basic Properties of the Wick Product / 5.3.1：
Hermite Transform and Characterization Theorem for (S)* / 5.3.2：
The Spaces G and G* / 5.3.3：
The Wick Product in Terms of Iterated Ito Integrals / 5.3.4：
Wick Products and Skorohod Integration / 5.3.5：
The Hida-Malliavin Derivative on the Space [Omega] = S'(R) / 5.4：
A New Definition of the Stochastic Gradient and a Generalized Chain Rule / 6.1：
Calculus of the Hida-Malliavin Derivative and Skorohod Integral / 6.2：
Wick Product vs. Ordinary Product / 6.2.1：
Closability of the Hida-Malliavin Derivative / 6.2.2：
Wick Chain Rule / 6.2.3：
Integration by Parts, Duality Formula, and Skorohod Isometry / 6.2.4：
Conditional Expectation on (S)* / 6.3：
Conditional Expectation on G* / 6.4：
A Generalized Clark-Ocone Theorem / 6.5：
The Donsker Delta Function and Applications / 6.6：
Motivation: An Application of the Donsker Delta Function to Hedging / 7.1：
The Donsker Delta Function / 7.2：
The Multidimensional Case / 7.3：
The Forward Integral and Applications / 7.4：
A Motivating Example / 8.1：
The Forward Integral / 8.2：
Ito Formula for Forward Integrals / 8.3：
Relation Between the forward Integral and Skorohod Integral / 8.4：
Ito Formula for Skorohod Integrals / 8.5：
Application to Insider Trading Modeling / 8.6：
Markets with No Friction / 8.6.1：
Markets with Friction / 8.6.2：
The Discontinuous Case: Pure Jummp Levy Processes / 8.7：
A Short Introduction to Levy Processes / 9：
Basics on Levy Processes / 9.1：
The Ito Formula / 9.2：
The Ito Representation Theorem for Pure Jump Levy Processes / 9.3：
Application to Finance: Replicability / 9.4：
Skorohod Integrals / 9.5：
Definition and Basic Properties / 11.1：
Integration by Parts and Closability of the Skorohod Integral / 12.2：
Fundamental Theorem of Calculus / 12.3.3：
A Combination of Gaussian and Pure Jump Levy Noises / 12.4：
Application of Minimal Variance Hedging with Partial Information / 12.6：
Computation of "Greeks" in the Case of Jump Diffusions / 12.7：
The Barndorff-Nielsen and Shephard Model / 12.7.1：
Malliavin Weights for "Greeks" / 12.7.2：
Levy White Noise and Stochastic Distributions / 12.8：
The White Noise Probability Space / 13.1：
An Alternative Chaos Expansion and the White Noise / 13.2：
The Wick Product / 13.3：
Definition and Properties / 13.3.1：
Wick Product and Skorohod Integral / 13.3.2：
Levy-Hermite Transform / 13.3.3：
Spaces of Smooth and Generalized Random Variables: G and G* / 13.4：
The Malliavin Derivative on G* / 13.5：
A Generalization of the Clark-Ocone Theorem / 13.6：
A Combination of Gaussian and Pure Jump Levy Noises in the White Noise Setting / 13.7：
Generalized Chain Rules for the Malliavin Derivative / 13.8：
The Donsker Delta Function of a Levy Process and Applications / 13.9：
The Donsker Delta Function of a Pure Jump Levy Process / 14.1：
An Explicit Formula for the Donsker Delta Function / 14.2：
Chaos Expansion of Local Time for Levy Processes / 14.3：
Application to Hedging in Incomplete Markets / 14.4：
A Sensitivity Result for Jump Diffusions / 14.5：
A Representation Theorem for Functions of a Class of Jump Diffusions / 14.5.1：
Application: Computation of the "Greeks" / 14.5.2：
Definition of Forward Integral and its Relation with the Skorohod Integral / 14.6：
Ito Formula for Forward and Skorohod Integrals / 15.2：
Applications to Stochastic Control: Partial and Inside Information / 15.3：
The Importance of Information in Portfolio Optimization / 16.1：
Optimal Portfolio Problem under Partial Information / 16.2：
Formalization of the Optimization Problem: General Utility Function / 16.2.1：
Characterization of an Optimal Portfolio Under Partial Information / 16.2.2：
Examples / 16.2.3：
Optimal Portfolio under Partial Information in an Anticipating Environment / 16.3：
The Continuous Case: Logarithmic Utility / 16.3.1：
The Pure Jump Case: Logarithmic Utility / 16.3.2：
A Universal Optimal Consumption Rate for an Insider / 16.4：
Formalization of a General Optimal Consumption Problem / 16.4.1：
Characterization of an Optimal Consumption Rate / 16.4.2：
Optimal Consumption and Portfolio / 16.4.3：
Optimal Portfolio Problem under Inside Information / 16.5：
Characterization of an Optimal Portfolio under Inside Information / 16.5.1：
Examples: General Utility and Enlargement of Filtration / 16.5.3：
Optimal Portfolio Problem under Inside Information: Logarithmic Utility / 16.6：
The Pure Jump Case / 16.6.1：
A Mixed Market Case / 16.6.2：
Examples: Enlargement of Filtration / 16.6.3：
Regularity of Solutions of SDEs Driven by Levy Processes / 16.7：
The General Case / 17.1：
Absolute Continuity of Probability Laws / 17.3：
Existence of Densities / 18.1：
Smooth Densities of Solutions to SDE's Driven by Levy Processes / 18.2：
Malliavin Calculus on the Wiener Space / 18.3：
Preliminary Basic Concepts / A.1：
Wiener Space, Cameron-Martin Space, and Stochastic Derivative / A.2：
Malliavin Derivative via Chaos Expansions / A.3：
Solutions
References
Notation and Symbols
Index
Introduction
The Continuous Case: Brownian Motion / Part I：
The Wiene-Ito Chaos Expansion / 1：
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