Oksendal, Bernt  | Springer

140,540원  | 20090810  | 9783540698258

Here is a rigorous introduction to solution methods of stochastic control problems for jump diffusions. The 2nd edition adds a chapter on optimal control of stochastic partial differential equations driven by Levy processes, and a section on optimal stopping with delayed information.

Oksendal, Bernt  | Springer

0원  | 20050130  | 9783540140238

The main purpose of the book is to give a rigorous, yet mostly nontechnical, introduction to the most important and useful solution methods of various types of stochastic control problems for jump diffusions and its applications. The types of control problems covered include classical stochastic control, optimal stopping, impulse control and singular control. Both the dynamic programming method and the maximum principle method are discussed, as well as the relation between them. Corresponding verification theorems involving the Hamilton-Jacobi Bellman equation and/or (quasi-)variational inequalities are formulated. There are also chapters on the viscosity solution formulation and numerical methods. The text emphasises applications, mostly to finance. All the main results are illustrated by examples and exercises appear at the end of each chapter with complete solutions. This will help the reader understand the theory and see how to apply it. The book assumes some basic knowledge of stochastic analysis, measure theory and partial differential equations.

Holden, Helge/Oksendal, Bernt/Uboe, Jan  | Springer

156,160원  | 20100924  | 9780387894874

The first edition of Stochastic Partial Differential Equations: A Modeling, White Noise Functional Approach, gave a comprehensive introduction to SPDEs. In this, the second edition, the authors build on the theory of SPDEs driven by space-time Brownian motion, or more generally, space-time Levy process noise. Applications of the theory are emphasized throughout. The stochastic pressure equation for fluid flow in porous media is treated, as are applications to finance.