利萨乌勒 calculus 对于金融学的应用及其在Lévy过程中的应用

While the original works on Malliavin calculus aimed to study the smoothness of densities of solutions to stochastic differential equations, this book has another goal. It portrays the most important and innovative applications in stochastic control and finance, such as hedging in complete and incomplete markets, optimisation in the presence of asymmetric information and also pricing and sensitivity analysis. In a self-contained fashion, both the Malliavin calculus with respect to Brownian motion and general Lévy type of noise are treated.

Besides, forward integration is included and indeed extended to general Lévy processes. The forward integration is a recent development within anticipative stochastic calculus that, together with the Malliavin calculus, provides new methods for the study of insider trading problems.

To allow more flexibility in the treatment of the mathematical tools, the generalization of Malliavin calculus to the white noise framework is also discussed.

This book is a valuable resource for graduate students, lecturers in stochastic analysis and applied researchers.

虽然原始的Malliavin微积分的研究旨在研究随机微分方程解的概率密度的光滑性，但本书的目标不同。它展示了在随机控制和金融领域中的最重要和最具创新的应用，例如完全市场和不完全市场的对冲、信息不对称情况下的优化问题以及定价与敏感性分析。

本书以自包含的方式处理了布朗运动及一般Lévy类型的噪声条件下的Malliavin微积分。

此外，还包括了前向积分，并且实际上扩展到了一般的Lévy过程。前向积分是前瞻随机微积分的一个近期发展，它与Malliavin微积分一起提供了解决内幕交易问题的新方法。

为了使处理数学工具时更具灵活性，还讨论了将Malliavin微积分推广到白噪声框架的方法。

本书对研究生、概率分析课程的讲师以及应用研究人员来说是一份宝贵的资源。

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