Malliavin Calculus for Lévy Processes with Applications to Finance
Publication year: 2009
ISBN: 978-3-540-78572-9
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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.
Subject: Mathematics and Statistics, Brownian motion, Levy processes, Lévy process, Malliavin calculus, Stochastic Differential Equations, Stochastic calculus, asymmetric information, calculus, optimization, stochastic control, white noise, quantitative finance
