描述
开 本: 24开纸 张: 胶版纸包 装: 平装是否套装: 否国际标准书号ISBN: 9787510058325
There are already several excellent books on Malliavin calculus. However， most of them deal only with the theory of Malliavin calculus for Brownian motion， with as an honorable exception. Moreover， most of them discuss only the application to regularity results for solutions of SDEs， as this was the original motivation when Paul Malliavin introduced the infinite-dimensional calculus in 1978 in. In the recent years， Malliavin calculus has found many applications in stochastic control and within finance. At the same time， Levy processes have become important in financial modeling. In view of this， we have seen the need for a book that deals with Malliavin calculus for Levy processes in general， not just Brownian motion， and that presents some of the most important and recent applications to finance.
Part I The Continuous Case: Brownian Motion
1 The Wiener-Ito Chaos Expansion
1.1 Iterated Ito Integrals
1.2 The Wiener-Ito Chaos Expansion
1.3 Exercises
2 The Skorohod Integral
2.1 The Skorohod Integral
2.2 Some Basic Properties of the Skorohod Integral
2.3 The Skorohod Integral as an Extension of the Ito Integral
2.4 Exercises
3 Malliavin Derivative via Chaos Expansion
3.1 The Malliavin Derivative
3.2 Computation and Properties of the Malliavin Derivative
3.2.1 Chain Rules for Malliavin Derrvative
3.2.2 Malliavin Derivative and Conditional Expectation
3.3 Malliavin Derivative and Skorohod Integral
3.3.1 Skorohod Integral as Adjoint Operator to theMalliavin Derivative
3.3.2 An Iritegration by Parts Formula and Closabilityof the Skorohod Integral
3.3.3 A Fundamental Theorem of Calculus
3.4 Exercises
4 Integral Representations and the Clark-Ocone Formula
4.1 The Clark-Ocone Formula
4.2 The Clark-Ocone Formula under Change of Measure
……
Part II The Discontinuous Case: Pure Ju~p L v Processes
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