Malliavin P., Thalmaier A. Stochastic Calculus of Variations in Mathematical Finance

Gaussian Stochastic Calculus of Variations.
Finite-Dimensional Gaussian Spaces.
Hermite Expansion.
Wiener Space as Limit of its Dyadic Filtration.
Stroock–Sobolev Spaces.
of Functionals on Wiener Space.
Divergence of Vector Fields, Integration by Parts.
Itˆo’s Theory of Stochastic Integrals.
Differential and Integral Calculus.
in Chaos Expansion.
Monte-Carlo Computation of Divergence.
Computation of Greeks.
and Integration by Parts Formulae.
PDE Option Pricing; PDEs Governing.
the Evolution of Greeks.
Stochastic Flow of Diffeomorphisms;
Ocone-Karatzas Hedging.
Principle of Equivalence of Instantaneous Derivatives.
Pathwise Smearing for European Options.
Examples of Computing Pathwise Weights.
Pathwise Smearing for Barrier Option.
Market Equilibrium and Price-Volatility Feedback Rate.
Natural Metric Associated to Pathwise Smearing.
Price-Volatility Feedback Rate.
Measurement of the Price-Volatility Feedback Rate.
Market Ergodicity.
and Price-Volatility Feedback Rate.
Multivariate Conditioning.
and Regularity of Law.
Non-Degenerate Maps.
Divergences.
Regularity of the Law of a Non-Degenerate Map.
Multivariate Conditioning.
Riesz Transform and Multivariate Conditioning.
Example of the Univariate Conditioning.
Non-Elliptic Markets and Instability.
in HJM Models.
Notation for Diffusions on RN.
The Malliavin Covariance Matrix.
of a Hypoelliptic Diffusion.
Malliavin Covariance Matrix.
and HЁormander Bracket Conditions.
Regularity by Predictable Smearing.
Forward Regularity.
by an Infinite-Dimensional Heat Equation.
Instability of Hedging Digital Options.
in HJM Models.
Econometric Observation of an Interest Rate Market.
Insider Trading.
A Toy Model: the Brownian Bridge.
Information Drift and Stochastic Calculus.
of Variations.
Integral Representation.
of Measure-Valued Martingales.
Insider Additional Utility.
An Example of an Insider Getting Free Lunches.
Asymptotic Expansion and Weak Convergence.
Asymptotic Expansion of SDEs Depending.
on a Parameter.
Watanabe Distributions and Descent Principle.
Strong Functional Convergence of the Euler Scheme.
Weak Convergence of the Euler Scheme.
Stochastic Calculus of Variations for Markets with Jumps.
Probability Spaces of Finite Type Jump Processes.
Stochastic Calculus of Variations.
for Exponential Variables.
Stochastic Calculus of Variations.
for Poisson Processes.
Mean-Variance Minimal Hedging.
and Clark–Ocone Formula.
A Volatility Estimation by Fourier Expansion.
A Fourier Transform of the Volatility Functor.
A Numerical Implementation of the Method.
B Strong Monte-Carlo Approximation.
of an Elliptic Market.
B Definition of the Scheme S.
B The Milstein Scheme.
B Horizontal Parametrization.
B Reconstruction of the Scheme S.
C Numerical Implementation.
of the Price-Volatility Feedback Rate.