金融作为商业的顶端，其发展更是离不开数学。本书就是一部版权引自国外的金融数学英文专著。 本书第一作者为法拉伊·朱利叶斯·马拉加，南非数学家，祖鲁兰大学教授。他在津巴布韦大学获得了数学硕士学位，并在开普敦大学取得博士学位，研究领域为数学金融。 本书包含了，马利亚万微积分的的基本性质、Greeks对连续过程计算的马利亚万微积分的应用、高斯过程白噪音微积分在Greeks计算中的应用、纯跳跃莱维SDEs的马利亚万微积分、针对跳跃扩散过程的Greeks的计算、莱维的白噪声微积分及其在Greeks计算中的应用等内容。

Abstract
Abstract
Dedication.
Acknowledgements
1 Introduction
1.1 Approaches to evaluating Greeks
1.2 Background on the Malliavin calculus
1.3 Aims and structure of the thesis
2 Basic Properties of the Malliavin calculus
2.1 Wiener Space
2.2 Malliavin derivative
2.3 Skorohod integral
2.4 SDEs and Malliavin calculus.
2.5 The integration by parts formula
2.6 Iterated Wiener-It? integrals .
2.7 Malliavin derivative via chaos expansion
2.8 Skorohod integral via chaos expansion
2.9 The Clark-Haussmann-Ocone formula
3 Application of Malliavin calculus to the Calculations of Greeks for Continuous Processes
3.1 Generalized Greeks
3.2 Greeks for European Options
3.3 Greeks for Exotic options
3.4 Greeks for Barriers and Look-back options.
3.5 Greeks for the Heston model
4 Application of white noise calculus for Gaussian Processes to the Calculs tion of Greeks
4.1 Basic concepts of Gaussian white noise analysis
4.2 Stochastic test functions and stochastic distribution functions
4.3 The Wick product
4.4 The Hermite Transform
4.5 Hida-Malliavin derivative
4.6 Conditional expectation on (S)*4.7 The Donsker delta function
4.8 Financial Application: Calculating Greeks
5 Malliavin calculus for Pure Jump Lévy SDEs
5.1 Basic definitions and results for Lévy processes
5.2 Chaos expansion
5.3 Skorohod integral
5.4 Stochastic derivative
5.5 Differentiability of pure jump Lévy stochastic differential equation
5.6 The necessary and sufficient condition for a function to serve as a weighting function
6 Calculations of Greeks for Jump Diffusion Processes
6.1 Basic elements of a Lévy chaotic calculus
6.2 Chaos expansion
6.2.1 Directional derivative
6.2.2 Wiener-Poisson space
6.3 Skorohod integral
6.4 Greeks for jump diffusion models
6.5 Greeks for the Heston model with jumps
6.6 Greeks for Lévy process
7 White noise calculus for Lévy Processes and its Application to the Calcu-lations of Greeks
7.1 Basic concepts of Lévy white noise analysis
7.2 Chaos expansion
7.3 The Hida/Kondratiev spaces
7.4 Lévy Wick product
7.5 Lévy Hermite transform
7.6 Lévy stochastic derivative
7.7 Donsker delta function of a Lévy process
7.8 Application: Computing Greeks
References
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