Stochastic calculus of variations in mathematical finance

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Stochastic calculus of variations in mathematical finance / Paul Malliavin, Anton Thalmaier

資料種別:

図書

出版情報:

Berlin : Springer, c2006

形態:

xi, 142 p. ; 24 cm

シリーズ名:

Springer finance <BA37506339>

著者名:

ISBN:

9783540434313 [3540434313]

書誌ID:

BA74246565

子書誌情報

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所蔵情報

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書誌詳細

注記:

Bibliography: p. [127]-138
Includes index

主題:

Finance--Mathematical models; Stochastic processes

言語:

英語

目次情報:

Gaussian Stochastic Calculus of Variations / 1：

Finite-Dimensional Gaussian Spaces, Hermite Expansion / 1.1：

Wiener Space as Limit of its Dyadic Filtration / 1.2：

Stroock-Sobolev Spaces of Functionals on Wiener Space / 1.3：

Divergence of Vector Fields, Integration by Parts / 1.4：

Ito's Theory of Stochastic Integrals / 1.5：

Differential and Integral Calculus in Chaos Expansion / 1.6：

Monte-Carlo Computation of Divergence / 1.7：

Computation of Greeks and Integration by Parts Formulae / 2：

PDE Option Pricing; PDEs Governing the Evolution of Greeks / 2.1：

Stochastic Flow of Diffeomorphisms; Ocone-Karatzas Hedging / 2.2：

Principle of Equivalence of Instantaneous Derivatives / 2.3：

Pathwise Smearing for European Options / 2.4：

Examples of Computing Pathwise Weights / 2.5：

Pathwise Smearing for Barrier Option / 2.6：

Market Equilibrium and Price-Volatility Feedback Rate / 3：

Natural Metric Associated to Pathwise Smearing / 3.1：

Price-Volatility Feedback Rate / 3.2：

Measurement of the Price-Volatility Feedback Rate / 3.3：

Market Ergodicity and Price-Volatility Feedback Rate / 3.4：

Multivariate Conditioning and Regularity of Law / 4：

Non-Degenerate Maps / 4.1：

Divergences / 4.2：

Regularity of the Law of a Non-Degenerate Map / 4.3：

Multivariate Conditioning / 4.4：

Riesz Transform and Multivariate Conditioning / 4.5：

Example of the Univariate Conditioning / 4.6：

Non-Elliptic Markets and Instability in HJM Models / 5：

Notation for Diffusions on R[superscript N] / 5.1：

The Malliavin Covariance Matrix of a Hypoelliptic Diffusion / 5.2：

Malliavin Covariance Matrix and Hormander Bracket Conditions / 5.3：

Regularity by Predictable Smearing / 5.4：

Forward Regularity by an Infinite-Dimensional Heat Equation / 5.5：

Instability of Hedging Digital Options in HJM Models / 5.6：

Econometric Observation of an Interest Rate Market / 5.7：

Insider Trading / 6：

A Toy Model: the Brownian Bridge / 6.1：

Information Drift and Stochastic Calculus of Variations / 6.2：

Integral Representation of Measure-Valued Martingales / 6.3：

Insider Additional Utility / 6.4：

An Example of an Insider Getting Free Lunches / 6.5：

Asymptotic Expansion and Weak Convergence / 7：

Asymptotic Expansion of SDEs Depending on a Parameter / 7.1：

Watanabe Distributions and Descent Principle / 7.2：

Strong Functional Convergence of the Euler Scheme / 7.3：

Weak Convergence of the Euler Scheme / 7.4：

Stochastic Calculus of Variations for Markets with Jumps / 8：

Probability Spaces of Finite Type Jump Processes / 8.1：

Stochastic Calculus of Variations for Exponential Variables / 8.2：

Stochastic Calculus of Variations for Poisson Processes / 8.3：

Mean-Variance Minimal Hedging and Clark-Ocone Formula / 8.4：

Volatility Estimation by Fourier Expansion / A：

Fourier Transform of the Volatility Functor / A.1：

Numerical Implementation of the Method / A.2：

Strong Monte-Carlo Approximation of an Elliptic Market / B：

Definition of the Scheme [characters not reproducible] / B.1：

The Milstein Scheme / B.2：

Horizontal Parametrization / B.3：

Reconstruction of the Scheme [characters not reproducible] / B.4：

Numerical Implementation of the Price-Volatility Feedback Rate / C：

References

Index

Gaussian Stochastic Calculus of Variations / 1：

Finite-Dimensional Gaussian Spaces, Hermite Expansion / 1.1：

Wiener Space as Limit of its Dyadic Filtration / 1.2：

Stroock-Sobolev Spaces of Functionals on Wiener Space / 1.3：

Divergence of Vector Fields, Integration by Parts / 1.4：

Ito's Theory of Stochastic Integrals / 1.5：

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