金融数学中的随机变分法
2007-5
北京世图
本社
142
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stochaLstic Calculus of Variations(or Malliavin Calculus)consists，in brief，in constructing and exploiting natural differentiable structures on abstract Drobability spaces；in other words，Stochastic Calculus of Variations proceeds from a merging of differential calculus and probability theory． As optimization under a random environment iS at the heart of mathemat’ical finance，and as differential calculus iS of paramount importance for the search of extrema，it is not surprising that Stochastic Calculus of Variations appears in mathematical finance．The computation of price sensitivities(orGreeksl obviously belongs to the realm of differential calculus． Nevertheless，Stochastic Calculus of Variations Was introduced relatively late in the mathematical finance literature：first in 1991 with the Ocone-Karatzas hedging formula，and soon after that，many other applications alDeared in various other branches of mathematical finance；in 1999 a new irapetus came from the works of P．L．Lions and his associates．
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 Divergence2 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 Option3 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 Rate4 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 Conditioning5 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 Market6 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 Lunches7 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 Scheme8 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 ExpansionB Strong Monte-Carlo ApproximationC Numerical ImplementationReferencesIndex
《金融数学中的随机变分法(英文版)》是一部金融数学名著，书中论述了随机分析理论及其与金融数学的关联性。目次如下：Gaussian随机变分；Greeks计算与分布积分公式；市场均衡与价格-挥发度反馈率；多元条件与分布律的正则化；非椭圆市场与HJM模型的不稳定性内部贸易；渐近展开与弱收敛跳跃市场的随机变分。附录：利用Fourier展式进行挥发评估；椭圆市场的Monte-Carlo强逼近；价格-挥发度反馈率的数值执行。
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malliavin写的随机变分，还有谁可以出其右？
买来收藏,不错的金融工程用书
提供了金融研究的方法
很好。自己会好好利用的。谢谢
这本教材属于springer的金融教材系列，但是阅读之前需要一定的数学基础，本科生读起来可能会有些困难，当然，不排除有人本科就很牛，不过最适合有读研意向的数学或金融类学生
数很薄。但是都是陌生的符号。没有一定数学基础的人，谨慎。
有一本书表皮破了