1 Gaussian Stochastic Calculus of Variations
1.1 Finite-Dimensional Gaussian Spaces, " Hermite Expansion
1.2 Wiener Space as Limit of its Dyadic Filtration
1.3 Stroock-Sobolev Spaces of Fnctionals on Wiener Space
1.4 Divergence of Vector Fields, Integration by Parts
1.5 ItS's Theory of Stochastic Integrals
1.6 Differential and Integral Calculus in Chaos Expansion
1.7 Monte-Carlo Computation of Divergence
2 Computation of Greeks and Integration by Parts Formulae
2.1 PDE Option Pricing; PDEs Governing the Evolution of Greeks
2.2 Stochastic Flow of Diffeomorphisms; Ocone-Karatzas Hedging
2.3 Principle of Equivalence of Instantaneous Derivatives
2.4 Pathwise Smearing for European Options
2.5 Examples of Computing Pathwise Weights
2.6 Pathwise Smearing for Barrier Option
3 Market Equilibrium and Price-Volatility Feedback Rate
3.1 Natural Metric Associated to Pathwise Smearin
3.2 Price-Volatility Feedback Rate
3.3 Measurement of the Price-Volatility Feedback Rate
3.4 Market Ergodicity and Price-Volatility Feedback Rate
4 Multivariate Conditioning and Regularity of Law
4.1 Non-Degenerate Maps
4.2 Divergences
4.3 Regularity of the Law of a Non-Degenerate Map
4.4 Multivariate Conditioning
4.5 Riesz Transform and Multivariate Conditioning
4.6 Example of the Univariate Conditioning
5 Non-Elliptic Markets and Instability in HJM Models
5.1 Notation for Diffusions on RN
5.2 The Malliavin Covariance Matrix of a Hypoelliptic Diffusion
5.3 Malliavin Covariance Matrix and HSrmander Bracket Conditions
5.4 Regularity by Predictable Smearing
5.5 Forward Regularity by an Infinite-Dimensional Heat Equation
5.6 Instability of Hedging Digital Options in HJM Models
5.7 Econometric Observation of an Interest Rate Market
6 Insider Trading
6.1 A Toy Model: the Brownian Bridge
6.2 Information Drift and Stochastic Calculus of Variations
6.3 Integral Representation of Measure-Valued Martingales
6.4 Insider Additional Utility
6.5 An Example of an Insider Getting Free Lunches
7 Asymptotic Expansion and Weak Convergence
7.1 Asymptotic Expansion of SDEs Depending on a Parameter
7.2 Watanabe Distributions and Descent Principle
7.3 Strong Functional Convergence of the Euler Scheme
7.4 Weak Convergence of the Euler Scheme
8 Stochastic Calculus of Variations for Markets with Jumps
8.1 Probability Spaces of Finite Type Jump Processes
8.2 Stochastic Calculus of Variations for Exponential Variables
8.3 Stochastic Calculus of Variations for Poisson Processes
……
A Volatility Estimation by Fourier Expansion
B Strong Monte-Carlo Approximation
C Numerical Implementation
References
Index
鄂公网安备 42010302001612号 