Series:

Universitext

3 total works

Cover of Applied Stochastic Control of Jump Diffusions
Here is a rigorous introduction to the most important and useful solution methods of various types of stochastic control problems for jump diffusions and its applications. Discussion includes the dynamic programming method and the maximum principle method, and their relationship. The text emphasises real-world applications, primarily in finance. Results are illustrated by examples, with end-of-chapter exercises including complete solutions. The 2nd edition adds a chapter on optimal control of stochastic partial differential equations driven by Levy processes, and a new section on optimal stopping with delayed information. Basic knowledge of stochastic analysis, measure theory and partial differential equations is assumed.

Cover of Stochastic Differential Equations
From the reviews: "The author, a lucid mind with a fine pedagogical instinct, has written a splendid text. He starts out by stating six problems in the introduction in which stochastic differential equations play an essential role in the solution. Then, while developing stochastic calculus, he frequently returns to these problems and variants thereof and to many other problems to show how the theory works and to motivate the next step in the theoretical development. Needless to say, he restricts himself to stochastic integration with respect to Brownian motion. He is not hesitant to give some basic results without proof in order to leave room for "some more basic applications...The book can be an ideal text for a graduate course, but it is also recommended to analysts (in particular, those working in differential equations and deterministic dynamical systems and control) who wish to learn quickly what stochastic differential equations are all about." Acta Scientiarum Mathematicarum, Tom 50, 3-4, 1986

Cover of Malliavin Calculus for Levy Processes with Applications to Finance
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 [35] as an honorable exception. Moreover, most of them discuss only the applicationto regularityresults for solutions ofSDEs, as this wasthe original motivation when Paul Malliavin introduced the in?nite-dimensional calculus in 1978 in [158]. In the recent years, Malliavin calculus has found many applications in stochastic control and within ?nance. At the same time, L' evy processes have become important in ?nancial modeling. In view of this, we have seen the need for a book that deals with Malliavin calculus for L' evy processesin general,not just Brownianmotion, and that presentssome of the most important and recent applications to ?nance. It is the purpose of this book to try to ?ll this need. In this monograph we present a general Malliavin calculus for L' evy processes, covering both the Brownianmotioncaseand the purejump martingalecasevia Poissonrandom measures,and also some combination of the two.